Metamath Proof Explorer


Theorem 1p8e9

Description: 1 + 8 = 9. (Contributed by SN, 24-Aug-2026)

Ref Expression
Assertion 1p8e9 ( 1 + 8 ) = 9

Proof

Step Hyp Ref Expression
1 df-8 ⊢ 8 = ( 7 + 1 )
2 1 oveq2i ⊢ ( 1 + 8 ) = ( 1 + ( 7 + 1 ) )
3 ax-1cn ⊢ 1 ∈ ℂ
4 7cn ⊢ 7 ∈ ℂ
5 3 4 3 addassi ⊢ ( ( 1 + 7 ) + 1 ) = ( 1 + ( 7 + 1 ) )
6 1p7e8 ⊢ ( 1 + 7 ) = 8
7 6 oveq1i ⊢ ( ( 1 + 7 ) + 1 ) = ( 8 + 1 )
8 8p1e9 ⊢ ( 8 + 1 ) = 9
9 7 8 eqtri ⊢ ( ( 1 + 7 ) + 1 ) = 9
10 2 5 9 3eqtr2i ⊢ ( 1 + 8 ) = 9