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 ∈ ℂ
4		2cn	⊢ 2 ∈ ℂ
5		ax-1cn	⊢ 1 ∈ ℂ
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