Theorem 5p5e10

Description: 5 + 5 = 10. (Contributed by NM, 5-Feb-2007) (Revised by Stanislas Polu, 7-Apr-2020) (Revised by AV, 6-Sep-2021)

	Ref	Expression
Assertion	5p5e10	$$⊢5+5=10$$

Proof

Step	Hyp	Ref	Expression
1		df-5	$$⊢5=4+1$$
2	1	oveq2i	$$⊢5+5=5+4+1$$
3		5cn	$$⊢5\in ℂ$$
4		4cn	$$⊢4\in ℂ$$
5		ax-1cn	$$⊢1\in ℂ$$
6	3 4 5	addassi	$$⊢5+4+1=5+4+1$$
7	2 6	eqtr4i	$$⊢5+5=5+4+1$$
8		5p4e9	$$⊢5+4=9$$
9	8	oveq1i	$$⊢5+4+1=9+1$$
10		9p1e10	$$⊢9+1=10$$
11	7 9 10	3eqtri	$$⊢5+5=10$$