Theorem 3p3e6

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

	Ref	Expression
Assertion	3p3e6	|- ( 3 + 3 ) = 6

Proof

Step	Hyp	Ref	Expression
1		df-3	|- 3 = ( 2 + 1 )
2	1	oveq2i	|- ( 3 + 3 ) = ( 3 + ( 2 + 1 ) )
3		3cn	|- 3 e. CC
4		2cn	|- 2 e. CC
5		ax-1cn	|- 1 e. CC
6	3 4 5	addassi	|- ( ( 3 + 2 ) + 1 ) = ( 3 + ( 2 + 1 ) )
7	2 6	eqtr4i	|- ( 3 + 3 ) = ( ( 3 + 2 ) + 1 )
8		df-6	|- 6 = ( 5 + 1 )
9		3p2e5	|- ( 3 + 2 ) = 5
10	9	oveq1i	|- ( ( 3 + 2 ) + 1 ) = ( 5 + 1 )
11	8 10	eqtr4i	|- 6 = ( ( 3 + 2 ) + 1 )
12	7 11	eqtr4i	|- ( 3 + 3 ) = 6