Theorem 8p2e10

Description: 8 + 2 = 10. (Contributed by NM, 5-Feb-2007) (Revised by Stanislas Polu, 7-Apr-2020) (Revised by AV, 6-Sep-2021)

	Ref	Expression
Assertion	8p2e10	|- ( 8 + 2 ) = ; 1 0

Proof

Step	Hyp	Ref	Expression
1		df-2	|- 2 = ( 1 + 1 )
2	1	oveq2i	|- ( 8 + 2 ) = ( 8 + ( 1 + 1 ) )
3		8cn	|- 8 e. CC
4		ax-1cn	|- 1 e. CC
5	3 4 4	addassi	|- ( ( 8 + 1 ) + 1 ) = ( 8 + ( 1 + 1 ) )
6	2 5	eqtr4i	|- ( 8 + 2 ) = ( ( 8 + 1 ) + 1 )
7		df-9	|- 9 = ( 8 + 1 )
8	7	oveq1i	|- ( 9 + 1 ) = ( ( 8 + 1 ) + 1 )
9		9p1e10	|- ( 9 + 1 ) = ; 1 0
10	6 8 9	3eqtr2i	|- ( 8 + 2 ) = ; 1 0