Metamath Proof Explorer


Theorem evenelz

Description: An even number is an integer. This follows immediately from the reverse closure of the divides relation, see dvdszrcl . (Contributed by AV, 22-Jun-2021)

Ref Expression
Assertion evenelz ⊢ 2 ∥ N → N ∈ ℤ

Proof

Step Hyp Ref Expression
1 dvdszrcl ⊢ 2 ∥ N → 2 ∈ ℤ ∧ N ∈ ℤ
2 1 simprd ⊢ 2 ∥ N → N ∈ ℤ