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 e. CC
4		5cn	|- 5 e. CC
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