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Metamath Proof Explorer

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	$⊢ 7 + 3 = 10$

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	$⊢ 7 + 3 = 10$