Metamath Proof Explorer


Theorem 2p5e7

Description: 2 + 5 = 7. (Contributed by SN, 24-Aug-2026)

Ref Expression
Assertion 2p5e7 ⊢ 2 + 5 = 7

Proof

Step Hyp Ref Expression
1 2cn ⊢ 2 ∈ ℂ
2 3cn ⊢ 3 ∈ ℂ
3 1 2 1 addassi ⊢ 2 + 3 + 2 = 2 + 3 + 2
4 2p3e5 ⊢ 2 + 3 = 5
5 4 oveq1i ⊢ 2 + 3 + 2 = 5 + 2
6 5p2e7 ⊢ 5 + 2 = 7
7 5 6 eqtri ⊢ 2 + 3 + 2 = 7
8 3p2e5 ⊢ 3 + 2 = 5
9 8 oveq2i ⊢ 2 + 3 + 2 = 2 + 5
10 3 7 9 3eqtr3ri ⊢ 2 + 5 = 7