Metamath Proof Explorer


Theorem 1p7e8

Description: 1 + 7 = 8. (Contributed by SN, 24-Aug-2026)

Ref Expression
Assertion 1p7e8 ( 1 + 7 ) = 8

Proof

Step Hyp Ref Expression
1 df-7 7 = ( 6 + 1 )
2 1 oveq2i ( 1 + 7 ) = ( 1 + ( 6 + 1 ) )
3 ax-1cn 1 ∈ ℂ
4 6cn 6 ∈ ℂ
5 3 4 3 addassi ( ( 1 + 6 ) + 1 ) = ( 1 + ( 6 + 1 ) )
6 1p6e7 ( 1 + 6 ) = 7
7 6 oveq1i ( ( 1 + 6 ) + 1 ) = ( 7 + 1 )
8 7p1e8 ( 7 + 1 ) = 8
9 7 8 eqtri ( ( 1 + 6 ) + 1 ) = 8
10 2 5 9 3eqtr2i ( 1 + 7 ) = 8