This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

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 )