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	$$⊢5\in ℂ$$
4		3cn	$$⊢3\in ℂ$$
5		ax-1cn	$$⊢1\in ℂ$$
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	$$⊢5+4=9$$