Theorem 7p2e9

Description: 7 + 2 = 9. (Contributed by NM, 11-May-2004)

	Ref	Expression
Assertion	7p2e9	|- ( 7 + 2 ) = 9

Proof

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