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

Metamath Proof Explorer

Theorem evenz

Description: An even number is an integer. (Contributed by AV, 14-Jun-2020)

Ref Expression
Assertion evenz ( 𝑍 ∈ Even → 𝑍 ∈ ℤ )

Proof

Step Hyp Ref Expression
1 iseven ⊢ ( 𝑍 ∈ Even ↔ ( 𝑍 ∈ ℤ ∧ ( 𝑍 / 2 ) ∈ ℤ ) )
2 1 simplbi ⊢ ( 𝑍 ∈ Even → 𝑍 ∈ ℤ )