Description: An even number is an integer. This follows immediately from the reverse closure of the divides relation, see dvdszrcl . (Contributed by AV, 22-Jun-2021)
Ref | Expression | ||
---|---|---|---|
Assertion | evenelz | ⊢ ( 2 ∥ 𝑁 → 𝑁 ∈ ℤ ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dvdszrcl | ⊢ ( 2 ∥ 𝑁 → ( 2 ∈ ℤ ∧ 𝑁 ∈ ℤ ) ) | |
2 | 1 | simprd | ⊢ ( 2 ∥ 𝑁 → 𝑁 ∈ ℤ ) |