Theorem 3p2e5

Description: 3 + 2 = 5. (Contributed by NM, 11-May-2004)

	Ref	Expression
Assertion	3p2e5	|- ( 3 + 2 ) = 5

Proof

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