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