Description: 2 does not divide 3. That means 3 is odd. (Contributed by AV, 28-Feb-2021) (Proof shortened by Steven Nguyen, 3-May-2023)
Ref | Expression | ||
---|---|---|---|
Assertion | n2dvds3 | ⊢ ¬ 2 ∥ 3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3halfnz | ⊢ ¬ ( 3 / 2 ) ∈ ℤ | |
2 | 3z | ⊢ 3 ∈ ℤ | |
3 | evend2 | ⊢ ( 3 ∈ ℤ → ( 2 ∥ 3 ↔ ( 3 / 2 ) ∈ ℤ ) ) | |
4 | 2 3 | ax-mp | ⊢ ( 2 ∥ 3 ↔ ( 3 / 2 ) ∈ ℤ ) |
5 | 1 4 | mtbir | ⊢ ¬ 2 ∥ 3 |