Description: Increasing an integer by 2 results in an integer. (Contributed by Alexander van der Vekens, 16-Sep-2018)
Ref | Expression | ||
---|---|---|---|
Assertion | zadd2cl | ⊢ ( 𝑁 ∈ ℤ → ( 𝑁 + 2 ) ∈ ℤ ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id | ⊢ ( 𝑁 ∈ ℤ → 𝑁 ∈ ℤ ) | |
2 | 2z | ⊢ 2 ∈ ℤ | |
3 | 2 | a1i | ⊢ ( 𝑁 ∈ ℤ → 2 ∈ ℤ ) |
4 | 1 3 | zaddcld | ⊢ ( 𝑁 ∈ ℤ → ( 𝑁 + 2 ) ∈ ℤ ) |