Theorem 4p4e8

Description: 4 + 4 = 8. (Contributed by NM, 11-May-2004)

	Ref	Expression
Assertion	4p4e8	⊢ ( 4 + 4 ) = 8

Proof

Step	Hyp	Ref	Expression
1		df-4	⊢ 4 = ( 3 + 1 )
2	1	oveq2i	⊢ ( 4 + 4 ) = ( 4 + ( 3 + 1 ) )
3		4cn	⊢ 4 ∈ ℂ
4		3cn	⊢ 3 ∈ ℂ
5		ax-1cn	⊢ 1 ∈ ℂ
6	3 4 5	addassi	⊢ ( ( 4 + 3 ) + 1 ) = ( 4 + ( 3 + 1 ) )
7	2 6	eqtr4i	⊢ ( 4 + 4 ) = ( ( 4 + 3 ) + 1 )
8		df-8	⊢ 8 = ( 7 + 1 )
9		4p3e7	⊢ ( 4 + 3 ) = 7
10	9	oveq1i	⊢ ( ( 4 + 3 ) + 1 ) = ( 7 + 1 )
11	8 10	eqtr4i	⊢ 8 = ( ( 4 + 3 ) + 1 )
12	7 11	eqtr4i	⊢ ( 4 + 4 ) = 8