Theorem flcld

Description: The floor (greatest integer) function is an integer (closure law). (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypothesis	flcld.1	$$⊢\phi \to A\in ℝ$$
Assertion	flcld	$$⊢\phi \to ⌊A⌋\in \mathbb{Z}$$

Proof

Step	Hyp	Ref	Expression
1		flcld.1	$$⊢\phi \to A\in ℝ$$
2		flcl	$$⊢A\in ℝ\to ⌊A⌋\in \mathbb{Z}$$
3	1 2	syl	$$⊢\phi \to ⌊A⌋\in \mathbb{Z}$$