Theorem 4p3e7

Description: 4 + 3 = 7. (Contributed by NM, 11-May-2004)

	Ref	Expression
Assertion	4p3e7	⊢ ( 4 + 3 ) = 7

Proof

Step	Hyp	Ref	Expression
1		df-3	⊢ 3 = ( 2 + 1 )
2	1	oveq2i	⊢ ( 4 + 3 ) = ( 4 + ( 2 + 1 ) )
3		4cn	⊢ 4 ∈ ℂ
4		2cn	⊢ 2 ∈ ℂ
5		ax-1cn	⊢ 1 ∈ ℂ
6	3 4 5	addassi	⊢ ( ( 4 + 2 ) + 1 ) = ( 4 + ( 2 + 1 ) )
7	2 6	eqtr4i	⊢ ( 4 + 3 ) = ( ( 4 + 2 ) + 1 )
8		df-7	⊢ 7 = ( 6 + 1 )
9		4p2e6	⊢ ( 4 + 2 ) = 6
10	9	oveq1i	⊢ ( ( 4 + 2 ) + 1 ) = ( 6 + 1 )
11	8 10	eqtr4i	⊢ 7 = ( ( 4 + 2 ) + 1 )
12	7 11	eqtr4i	⊢ ( 4 + 3 ) = 7