Theorem oddz

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

	Ref	Expression
Assertion	oddz	⊢ ( 𝑍 ∈ Odd → 𝑍 ∈ ℤ )

Proof

Step	Hyp	Ref	Expression
1		isodd	⊢ ( 𝑍 ∈ Odd ↔ ( 𝑍 ∈ ℤ ∧ ( ( 𝑍 + 1 ) / 2 ) ∈ ℤ ) )
2	1	simplbi	⊢ ( 𝑍 ∈ Odd → 𝑍 ∈ ℤ )