Description: A positive integer is even or odd but not both. (Contributed by NM, 20-Aug-2001)
Ref | Expression | ||
---|---|---|---|
Hypothesis | nneoi.1 | ⊢ 𝑁 ∈ ℕ | |
Assertion | nneoi | ⊢ ( ( 𝑁 / 2 ) ∈ ℕ ↔ ¬ ( ( 𝑁 + 1 ) / 2 ) ∈ ℕ ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nneoi.1 | ⊢ 𝑁 ∈ ℕ | |
2 | nneo | ⊢ ( 𝑁 ∈ ℕ → ( ( 𝑁 / 2 ) ∈ ℕ ↔ ¬ ( ( 𝑁 + 1 ) / 2 ) ∈ ℕ ) ) | |
3 | 1 2 | ax-mp | ⊢ ( ( 𝑁 / 2 ) ∈ ℕ ↔ ¬ ( ( 𝑁 + 1 ) / 2 ) ∈ ℕ ) |