Metamath Proof Explorer


Theorem 5p4e9

Description: 5 + 4 = 9. (Contributed by NM, 11-May-2004)

Ref Expression
Assertion 5p4e9 ⊢ 5 + 4 = 9

Proof

Step Hyp Ref Expression
1 df-4 ⊢ 4 = 3 + 1
2 1 oveq2i ⊢ 5 + 4 = 5 + 3 + 1
3 5cn ⊢ 5 ∈ ℂ
4 3cn ⊢ 3 ∈ ℂ
5 ax-1cn ⊢ 1 ∈ ℂ
6 3 4 5 addassi ⊢ 5 + 3 + 1 = 5 + 3 + 1
7 2 6 eqtr4i ⊢ 5 + 4 = 5 + 3 + 1
8 df-9 ⊢ 9 = 8 + 1
9 5p3e8 ⊢ 5 + 3 = 8
10 9 oveq1i ⊢ 5 + 3 + 1 = 8 + 1
11 8 10 eqtr4i ⊢ 9 = 5 + 3 + 1
12 7 11 eqtr4i ⊢ 5 + 4 = 9