diff --git a/DESCRIPTION b/DESCRIPTION
index 1ae5d3a..b33e80c 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -20,8 +20,8 @@ Suggests:
     rstudioapi,
     tinytex (>= 0.30),
     mime,
-    markdown,
-    knitr,
+    markdown (>= 1.5),
+    knitr (>= 1.42),
     htmltools,
     remotes,
     pak,
diff --git a/NEWS.md b/NEWS.md
index 41ed877..f841ae6 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -2,6 +2,8 @@
 
 - Added a function `is_arm64()` to test the CPU type (thanks, @AlbanSagouis, #72).
 
+- Started deprecating `xfun::isFALSE()` in favor of `base::isFALSE()` for R >= 3.5.0 (thanks, @mmaechler, #66); `isFALSE()` will eventually be removed from **xfun** when we do not need to support R < 3.5.0.
+
 # CHANGES IN xfun VERSION 0.36
 
 - Added a new argument `resolve_symlink` to `normalize_path()` to get the absolute paths of symlinks without resolving them (with `resolve_symlink = FALSE`).
diff --git a/R/packages.R b/R/packages.R
index 38ef2ef..17770b6 100644
--- a/R/packages.R
+++ b/R/packages.R
@@ -47,7 +47,7 @@ pkg_attach = function(
     suppressPackageStartupMessages(base::library(...))
   }
   for (i in c(...)) {
-    if (!isFALSE(install) && !loadable(i)) pkg_install(i, install)
+    if (!base::isFALSE(install) && !loadable(i)) pkg_install(i, install)
     library(i, character.only = TRUE)
   }
 }
@@ -60,7 +60,7 @@ pkg_load = function(..., error = TRUE, install = FALSE) {
   if (n == 0) return(invisible(res))
   for (i in seq_len(n)) {
     res[i] = loadable(p <- pkg[i])
-    if (!isFALSE(install) && !res[i]) {
+    if (!base::isFALSE(install) && !res[i]) {
       pkg_install(p, install); res[i] = loadable(p)
     }
   }
diff --git a/R/paths.R b/R/paths.R
index 4ded25a..7f7d2f9 100644
--- a/R/paths.R
+++ b/R/paths.R
@@ -123,7 +123,7 @@ existing_files = function(x, first = FALSE, error = TRUE) {
   x = x[file_exists(x)]
   if (!first) return(x)
   x = head(x, 1)
-  if (length(x) != 1 && !isFALSE(error)) {
+  if (length(x) != 1 && !base::isFALSE(error)) {
     if (isTRUE(error)) error = 'None of the specified files exist.'
     stop(error, call. = FALSE)
   }
diff --git a/R/session.R b/R/session.R
index 8ae7c90..7f12f8d 100644
--- a/R/session.R
+++ b/R/session.R
@@ -106,7 +106,7 @@ do_once = function(task, option, hint = c(
   'If you never want to see this message,',
   sprintf('you may set options(%s = FALSE) in your .Rprofile.', option)
 )) {
-  if (isFALSE(getOption(option))) return(invisible())
+  if (base::isFALSE(getOption(option))) return(invisible())
   task
   hint = paste(hint, collapse = ' ')
   if (hint != '') message(hint)
diff --git a/R/utils.R b/R/utils.R
index 168b139..d4acb06 100644
--- a/R/utils.R
+++ b/R/utils.R
@@ -90,17 +90,31 @@ in_dir = function(dir, expr) {
   expr
 }
 
-#' Test if an object is identical to \code{FALSE}
+#' Test if an object is \code{FALSE}
 #'
-#' A simple abbreviation of \code{identical(x, FALSE)}.
+#' For R versions lower than 3.5.0, this function is a simple abbreviation of
+#' \code{identical(x, FALSE)}. For higher R versions, this function calls
+#' \code{base::isFALSE()}.
 #' @param x An R object.
+#' @note This function will be deprecated in the future. We recommend that you
+#'   use \code{base::\link[base]{isFALSE}()} instead. If you have to support R
+#'   versions lower than 3.5.0, you may use \code{identical(x, FALSE)}, but
+#'   please note that it is not equivalent to \code{base::isFALSE()}.
 #' @export
-#' @examples
+#' @keywords internal
+#' @examplesIf getRversion() < '3.5.0'
 #' library(xfun)
 #' isFALSE(TRUE)  # false
 #' isFALSE(FALSE)  # true
 #' isFALSE(c(FALSE, FALSE))  # false
-isFALSE = function(x) identical(x, FALSE)
+isFALSE = function(x) {
+  if (!('isFALSE' %in% ls(baseenv()))) return(identical(x, FALSE))
+  do_once((if (is_R_CMD_check()) stop else warning)(
+    'The function xfun::isFALSE() will be deprecated in the future. Please ',
+    'consider using base::isFALSE(x) or identical(x, FALSE) instead.'
+  ), 'xfun.isFALSE.message', '')
+  base::isFALSE(x)
+}
 
 #' Parse R code and do not keep the source
 #'
diff --git a/man/isFALSE.Rd b/man/isFALSE.Rd
index a9074fe..d2395d3 100644
--- a/man/isFALSE.Rd
+++ b/man/isFALSE.Rd
@@ -2,7 +2,7 @@
 % Please edit documentation in R/utils.R
 \name{isFALSE}
 \alias{isFALSE}
-\title{Test if an object is identical to \code{FALSE}}
+\title{Test if an object is \code{FALSE}}
 \usage{
 isFALSE(x)
 }
@@ -10,11 +10,21 @@ isFALSE(x)
 \item{x}{An R object.}
 }
 \description{
-A simple abbreviation of \code{identical(x, FALSE)}.
+For R versions lower than 3.5.0, this function is a simple abbreviation of
+\code{identical(x, FALSE)}. For higher R versions, this function calls
+\code{base::isFALSE()}.
 }
-\examples{
+\note{
+This function will be deprecated in the future. We recommend that you
+  use \code{base::\link[base]{isFALSE}()} instead. If you have to support R
+  versions lower than 3.5.0, you may use \code{identical(x, FALSE)}, but
+  please note that it is not equivalent to \code{base::isFALSE()}.
+}
+\examples{\dontshow{if (getRversion() < '3.5.0') (if (getRversion() >= "3.4") withAutoprint else force)(\{ # examplesIf}
 library(xfun)
 isFALSE(TRUE)  # false
 isFALSE(FALSE)  # true
 isFALSE(c(FALSE, FALSE))  # false
+\dontshow{\}) # examplesIf}
 }
+\keyword{internal}