Metamath Proof Explorer


Theorem add1p1

Description: Adding two times 1 to a number. (Contributed by AV, 22-Sep-2018)

Ref Expression
Assertion add1p1 ⊢ N ∈ ℂ → N + 1 + 1 = N + 2

Proof

Step Hyp Ref Expression
1 id ⊢ N ∈ ℂ → N ∈ ℂ
2 1cnd ⊢ N ∈ ℂ → 1 ∈ ℂ
3 1 2 2 addassd ⊢ N ∈ ℂ → N + 1 + 1 = N + 1 + 1
4 1p1e2 ⊢ 1 + 1 = 2
5 4 a1i ⊢ N ∈ ℂ → 1 + 1 = 2
6 5 oveq2d ⊢ N ∈ ℂ → N + 1 + 1 = N + 2
7 3 6 eqtrd ⊢ N ∈ ℂ → N + 1 + 1 = N + 2