This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem reflcl

Description: The floor (greatest integer) function is real. (Contributed by NM, 15-Jul-2008)

		Ref	Expression
	Assertion	reflcl	$⊢ A \in ℝ \to ⌊A⌋ \in ℝ$

Step	Hyp	Ref	Expression
1		flcl	$⊢ A \in ℝ \to ⌊A⌋ \in ℤ$
2	1	zred	$⊢ A \in ℝ \to ⌊A⌋ \in ℝ$