Metamath Proof Explorer


Theorem 8p2e10

Description: 8 + 2 = 10. (Contributed by NM, 5-Feb-2007) (Revised by Stanislas Polu, 7-Apr-2020) (Revised by AV, 6-Sep-2021)

Ref Expression
Assertion 8p2e10 ⊢ 8 + 2 = 10

Proof

Step Hyp Ref Expression
1 df-2 ⊢ 2 = 1 + 1
2 1 oveq2i ⊢ 8 + 2 = 8 + 1 + 1
3 8cn ⊢ 8 ∈ ℂ
4 ax-1cn ⊢ 1 ∈ ℂ
5 3 4 4 addassi ⊢ 8 + 1 + 1 = 8 + 1 + 1
6 2 5 eqtr4i ⊢ 8 + 2 = 8 + 1 + 1
7 df-9 ⊢ 9 = 8 + 1
8 7 oveq1i ⊢ 9 + 1 = 8 + 1 + 1
9 9p1e10 ⊢ 9 + 1 = 10
10 6 8 9 3eqtr2i ⊢ 8 + 2 = 10