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	|- ( ph -> A e. RR )
Assertion	flcld	|- ( ph -> ( |_ ` A ) e. ZZ )

Proof

Step	Hyp	Ref	Expression
1		flcld.1	|- ( ph -> A e. RR )
2		flcl	|- ( A e. RR -> ( |_ ` A ) e. ZZ )
3	1 2	syl	|- ( ph -> ( |_ ` A ) e. ZZ )