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 )