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

Metamath Proof Explorer

Theorem eluzelzd

Description: A member of an upper set of integers is an integer. (Contributed by Glauco Siliprandi, 8-Apr-2021)

Ref Expression
Hypothesis eluzelzd.1 ⊢ ( 𝜑 → 𝑁 ∈ ( ℤ≥ ‘ 𝑀 ) )
Assertion eluzelzd ( 𝜑 → 𝑁 ∈ ℤ )

Proof

Step Hyp Ref Expression
1 eluzelzd.1 ⊢ ( 𝜑 → 𝑁 ∈ ( ℤ≥ ‘ 𝑀 ) )
2 eluzelz ⊢ ( 𝑁 ∈ ( ℤ≥ ‘ 𝑀 ) → 𝑁 ∈ ℤ )
3 1 2 syl ⊢ ( 𝜑 → 𝑁 ∈ ℤ )