Metamath Proof Explorer


Theorem 7p2e9

Description: 7 + 2 = 9. (Contributed by NM, 11-May-2004)

Ref Expression
Assertion 7p2e9 ⊢ 7 + 2 = 9

Proof

Step Hyp Ref Expression
1 df-2 ⊢ 2 = 1 + 1
2 1 oveq2i ⊢ 7 + 2 = 7 + 1 + 1
3 7cn ⊢ 7 ∈ ℂ
4 ax-1cn ⊢ 1 ∈ ℂ
5 3 4 4 addassi ⊢ 7 + 1 + 1 = 7 + 1 + 1
6 2 5 eqtr4i ⊢ 7 + 2 = 7 + 1 + 1
7 df-8 ⊢ 8 = 7 + 1
8 7 oveq1i ⊢ 8 + 1 = 7 + 1 + 1
9 6 8 eqtr4i ⊢ 7 + 2 = 8 + 1
10 df-9 ⊢ 9 = 8 + 1
11 9 10 eqtr4i ⊢ 7 + 2 = 9