Metamath Proof Explorer


Theorem 1p6e7

Description: 1 + 6 = 7. (Contributed by SN, 24-Aug-2026)

Ref Expression
Assertion 1p6e7 ( 1 + 6 ) = 7

Proof

Step Hyp Ref Expression
1 df-6 ⊢ 6 = ( 5 + 1 )
2 1 oveq2i ⊢ ( 1 + 6 ) = ( 1 + ( 5 + 1 ) )
3 ax-1cn ⊢ 1 ∈ ℂ
4 5cn ⊢ 5 ∈ ℂ
5 3 4 3 addassi ⊢ ( ( 1 + 5 ) + 1 ) = ( 1 + ( 5 + 1 ) )
6 1p5e6 ⊢ ( 1 + 5 ) = 6
7 6 oveq1i ⊢ ( ( 1 + 5 ) + 1 ) = ( 6 + 1 )
8 6p1e7 ⊢ ( 6 + 1 ) = 7
9 7 8 eqtri ⊢ ( ( 1 + 5 ) + 1 ) = 7
10 2 5 9 3eqtr2i ⊢ ( 1 + 6 ) = 7