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Metamath Proof Explorer

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 )