Theorem reflcl

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

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

Proof

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