Theorem 5p4e9

Description: 5 + 4 = 9. (Contributed by NM, 11-May-2004)

	Ref	Expression
Assertion	5p4e9	|- ( 5 + 4 ) = 9

Proof

Step	Hyp	Ref	Expression
1		df-4	|- 4 = ( 3 + 1 )
2	1	oveq2i	|- ( 5 + 4 ) = ( 5 + ( 3 + 1 ) )
3		5cn	|- 5 e. CC
4		3cn	|- 3 e. CC
5		ax-1cn	|- 1 e. CC
6	3 4 5	addassi	|- ( ( 5 + 3 ) + 1 ) = ( 5 + ( 3 + 1 ) )
7	2 6	eqtr4i	|- ( 5 + 4 ) = ( ( 5 + 3 ) + 1 )
8		df-9	|- 9 = ( 8 + 1 )
9		5p3e8	|- ( 5 + 3 ) = 8
10	9	oveq1i	|- ( ( 5 + 3 ) + 1 ) = ( 8 + 1 )
11	8 10	eqtr4i	|- 9 = ( ( 5 + 3 ) + 1 )
12	7 11	eqtr4i	|- ( 5 + 4 ) = 9