Theorem 5p4e9

Description: 5 + 4 = 9. (Contributed by NM, 11-May-2004)

	Ref	Expression
Assertion	5p4e9	⊢ ( 5 + 4 ) = 9

Proof

Step	Hyp	Ref	Expression
1		df-4	⊢ 4 = ( 3 + 1 )
2	1	oveq2i	⊢ ( 5 + 4 ) = ( 5 + ( 3 + 1 ) )
3		5cn	⊢ 5 ∈ ℂ
4		3cn	⊢ 3 ∈ ℂ
5		ax-1cn	⊢ 1 ∈ ℂ
6	3 4 5	addassi	⊢ ( ( 5 + 3 ) + 1 ) = ( 5 + ( 3 + 1 ) )
7	2 6	eqtr4i	⊢ ( 5 + 4 ) = ( ( 5 + 3 ) + 1 )
8		df-9	⊢ 9 = ( 8 + 1 )
9		5p3e8	⊢ ( 5 + 3 ) = 8
10	9	oveq1i	⊢ ( ( 5 + 3 ) + 1 ) = ( 8 + 1 )
11	8 10	eqtr4i	⊢ 9 = ( ( 5 + 3 ) + 1 )
12	7 11	eqtr4i	⊢ ( 5 + 4 ) = 9