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 = ( ℤ𝑀 )
eluzelz2d.2 ( 𝜑𝑁𝑍 )
Assertion eluzelz2d ( 𝜑𝑁 ∈ ℤ )

Proof

Step Hyp Ref Expression
1 eluzelz2d.1 𝑍 = ( ℤ𝑀 )
2 eluzelz2d.2 ( 𝜑𝑁𝑍 )
3 1 eluzelz2 ( 𝑁𝑍𝑁 ∈ ℤ )
4 2 3 syl ( 𝜑𝑁 ∈ ℤ )