Theorem eluzelz2d

Description: A member of an upper set of integers is an integer. (Contributed by Glauco Siliprandi, 23-Oct-2021)

	Ref	Expression
Hypotheses	eluzelz2d.1	|- Z = ( ZZ>= ` M )
	eluzelz2d.2	|- ( ph -> N e. Z )
Assertion	eluzelz2d	|- ( ph -> N e. ZZ )

Proof

Step	Hyp	Ref	Expression
1		eluzelz2d.1	|- Z = ( ZZ>= ` M )
2		eluzelz2d.2	|- ( ph -> N e. Z )
3	1	eluzelz2	|- ( N e. Z -> N e. ZZ )
4	2 3	syl	|- ( ph -> N e. ZZ )