Theorem 6p3e9

Description: 6 + 3 = 9. (Contributed by NM, 11-May-2004)

	Ref	Expression
Assertion	6p3e9	|- ( 6 + 3 ) = 9

Proof

Step	Hyp	Ref	Expression
1		df-3	|- 3 = ( 2 + 1 )
2	1	oveq2i	|- ( 6 + 3 ) = ( 6 + ( 2 + 1 ) )
3		6cn	|- 6 e. CC
4		2cn	|- 2 e. CC
5		ax-1cn	|- 1 e. CC
6	3 4 5	addassi	|- ( ( 6 + 2 ) + 1 ) = ( 6 + ( 2 + 1 ) )
7	2 6	eqtr4i	|- ( 6 + 3 ) = ( ( 6 + 2 ) + 1 )
8		df-9	|- 9 = ( 8 + 1 )
9		6p2e8	|- ( 6 + 2 ) = 8
10	9	oveq1i	|- ( ( 6 + 2 ) + 1 ) = ( 8 + 1 )
11	8 10	eqtr4i	|- 9 = ( ( 6 + 2 ) + 1 )
12	7 11	eqtr4i	|- ( 6 + 3 ) = 9