Theorem 2ndvdsodd

Description: 2 does not divide an odd number. (Contributed by AV, 18-Jun-2020)

	Ref	Expression
Assertion	2ndvdsodd	⊢ ( 𝑍 ∈ Odd → ¬ 2 ∥ 𝑍 )

Proof

Step	Hyp	Ref	Expression
1		isodd3	⊢ ( 𝑍 ∈ Odd ↔ ( 𝑍 ∈ ℤ ∧ ¬ 2 ∥ 𝑍 ) )
2	1	simprbi	⊢ ( 𝑍 ∈ Odd → ¬ 2 ∥ 𝑍 )