This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

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 = ℤ ≥ M
eluzelz2d.2 ⊢ φ → N ∈ Z
Assertion eluzelz2d ⊢ φ → N ∈ ℤ

Proof

Step Hyp Ref Expression
1 eluzelz2d.1 ⊢ Z = ℤ ≥ M
2 eluzelz2d.2 ⊢ φ → N ∈ Z
3 1 eluzelz2 ⊢ N ∈ Z → N ∈ ℤ
4 2 3 syl ⊢ φ → N ∈ ℤ