Metamath Proof Explorer


Theorem 3p4e7

Description: 3 + 4 = 7. (Contributed by SN, 24-Aug-2026)

Ref Expression
Assertion 3p4e7 ( 3 + 4 ) = 7

Proof

Step Hyp Ref Expression
1 3cn ⊢ 3 ∈ ℂ
2 2cn ⊢ 2 ∈ ℂ
3 1 2 2 addassi ⊢ ( ( 3 + 2 ) + 2 ) = ( 3 + ( 2 + 2 ) )
4 3p2e5 ⊢ ( 3 + 2 ) = 5
5 4 oveq1i ⊢ ( ( 3 + 2 ) + 2 ) = ( 5 + 2 )
6 5p2e7 ⊢ ( 5 + 2 ) = 7
7 5 6 eqtri ⊢ ( ( 3 + 2 ) + 2 ) = 7
8 2p2e4 ⊢ ( 2 + 2 ) = 4
9 8 oveq2i ⊢ ( 3 + ( 2 + 2 ) ) = ( 3 + 4 )
10 3 7 9 3eqtr3ri ⊢ ( 3 + 4 ) = 7