Theorem 6p2e8

Description: 6 + 2 = 8. (Contributed by NM, 11-May-2004)

	Ref	Expression
Assertion	6p2e8	|- ( 6 + 2 ) = 8

Proof

Step	Hyp	Ref	Expression
1		df-2	|- 2 = ( 1 + 1 )
2	1	oveq2i	|- ( 6 + 2 ) = ( 6 + ( 1 + 1 ) )
3		6cn	|- 6 e. CC
4		ax-1cn	|- 1 e. CC
5	3 4 4	addassi	|- ( ( 6 + 1 ) + 1 ) = ( 6 + ( 1 + 1 ) )
6	2 5	eqtr4i	|- ( 6 + 2 ) = ( ( 6 + 1 ) + 1 )
7		df-7	|- 7 = ( 6 + 1 )
8	7	oveq1i	|- ( 7 + 1 ) = ( ( 6 + 1 ) + 1 )
9	6 8	eqtr4i	|- ( 6 + 2 ) = ( 7 + 1 )
10		df-8	|- 8 = ( 7 + 1 )
11	9 10	eqtr4i	|- ( 6 + 2 ) = 8