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

Metamath Proof Explorer

Theorem 2dvdseven

Description: 2 divides an even number. (Contributed by AV, 18-Jun-2020)

Ref Expression
Assertion 2dvdseven ( 𝑍 ∈ Even → 2 ∥ 𝑍 )

Proof

Step Hyp Ref Expression
1 iseven2 ⊢ ( 𝑍 ∈ Even ↔ ( 𝑍 ∈ ℤ ∧ 2 ∥ 𝑍 ) )
2 1 simprbi ⊢ ( 𝑍 ∈ Even → 2 ∥ 𝑍 )