Theorem evendiv2z

Description: The result of dividing an even number by 2 is an integer. (Contributed by AV, 15-Jun-2020)

	Ref	Expression
Assertion	evendiv2z	⊢ ( 𝑍 ∈ Even → ( 𝑍 / 2 ) ∈ ℤ )

Proof

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