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 )