Metamath Proof Explorer


Theorem elfzelzd

Description: A member of a finite set of sequential integers is an integer. (Contributed by Glauco Siliprandi, 5-Apr-2020)

Ref Expression
Hypothesis elfzelzd.1 ⊢ φ → K ∈ M … N
Assertion elfzelzd ⊢ φ → K ∈ ℤ

Proof

Step Hyp Ref Expression
1 elfzelzd.1 ⊢ φ → K ∈ M … N
2 elfzelz ⊢ K ∈ M … N → K ∈ ℤ
3 1 2 syl ⊢ φ → K ∈ ℤ