Theorem 4p4e8

Description: 4 + 4 = 8. (Contributed by NM, 11-May-2004)

	Ref	Expression
Assertion	4p4e8	|- ( 4 + 4 ) = 8

Proof

Step	Hyp	Ref	Expression
1		df-4	|- 4 = ( 3 + 1 )
2	1	oveq2i	|- ( 4 + 4 ) = ( 4 + ( 3 + 1 ) )
3		4cn	|- 4 e. CC
4		3cn	|- 3 e. CC
5		ax-1cn	|- 1 e. CC
6	3 4 5	addassi	|- ( ( 4 + 3 ) + 1 ) = ( 4 + ( 3 + 1 ) )
7	2 6	eqtr4i	|- ( 4 + 4 ) = ( ( 4 + 3 ) + 1 )
8		df-8	|- 8 = ( 7 + 1 )
9		4p3e7	|- ( 4 + 3 ) = 7
10	9	oveq1i	|- ( ( 4 + 3 ) + 1 ) = ( 7 + 1 )
11	8 10	eqtr4i	|- 8 = ( ( 4 + 3 ) + 1 )
12	7 11	eqtr4i	|- ( 4 + 4 ) = 8