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Metamath Proof Explorer
Description: A positive integer is even or odd but not both. (Contributed by NM, 1-Jan-2006) (Revised by AV, 19-Jun-2020)
|
|
Ref |
Expression |
|
Assertion |
nneoALTV |
⊢ ( 𝑁 ∈ ℕ → ( 𝑁 ∈ Even ↔ ¬ 𝑁 ∈ Odd ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
nnz |
⊢ ( 𝑁 ∈ ℕ → 𝑁 ∈ ℤ ) |
| 2 |
|
zeo2ALTV |
⊢ ( 𝑁 ∈ ℤ → ( 𝑁 ∈ Even ↔ ¬ 𝑁 ∈ Odd ) ) |
| 3 |
1 2
|
syl |
⊢ ( 𝑁 ∈ ℕ → ( 𝑁 ∈ Even ↔ ¬ 𝑁 ∈ Odd ) ) |