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 )