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Metamath Proof Explorer

Theorem nneoiALTV

Description: A positive integer is even or odd but not both. (Contributed by NM, 20-Aug-2001) (Revised by AV, 19-Jun-2020)

Ref Expression
Hypothesis nneoiALTV.1 ⊢ 𝑁 ∈ ℕ
Assertion nneoiALTV ( 𝑁 ∈ Even ↔ ¬ 𝑁 ∈ Odd )

Proof

Step Hyp Ref Expression
1 nneoiALTV.1 ⊢ 𝑁 ∈ ℕ
2 nneoALTV ⊢ ( 𝑁 ∈ ℕ → ( 𝑁 ∈ Even ↔ ¬ 𝑁 ∈ Odd ) )
3 1 2 ax-mp ⊢ ( 𝑁 ∈ Even ↔ ¬ 𝑁 ∈ Odd )