Theorem 7p3e10

Description: 7 + 3 = 10. (Contributed by NM, 5-Feb-2007) (Revised by Stanislas Polu, 7-Apr-2020) (Revised by AV, 6-Sep-2021)

	Ref	Expression
Assertion	7p3e10	$$⊢7+3=10$$

Proof

Step	Hyp	Ref	Expression
1		df-3	$$⊢3=2+1$$
2	1	oveq2i	$$⊢7+3=7+2+1$$
3		7cn	$$⊢7\in ℂ$$
4		2cn	$$⊢2\in ℂ$$
5		ax-1cn	$$⊢1\in ℂ$$
6	3 4 5	addassi	$$⊢7+2+1=7+2+1$$
7	2 6	eqtr4i	$$⊢7+3=7+2+1$$
8		7p2e9	$$⊢7+2=9$$
9	8	oveq1i	$$⊢7+2+1=9+1$$
10		9p1e10	$$⊢9+1=10$$
11	7 9 10	3eqtri	$$⊢7+3=10$$