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Metamath Proof Explorer

Theorem 8p2e10

Description: 8 + 2 = 10. (Contributed by NM, 5-Feb-2007) (Revised by Stanislas Polu, 7-Apr-2020) (Revised by AV, 6-Sep-2021)

		Ref	Expression
	Assertion	8p2e10	$⊢ 8 + 2 = 10$

Step	Hyp	Ref	Expression
1		df-2	$⊢ 2 = 1 + 1$
2	1	oveq2i	$⊢ 8 + 2 = 8 + 1 + 1$
3		8cn	$⊢ 8 \in ℂ$
4		ax-1cn	$⊢ 1 \in ℂ$
5	3 4 4	addassi	$⊢ 8 + 1 + 1 = 8 + 1 + 1$
6	2 5	eqtr4i	$⊢ 8 + 2 = 8 + 1 + 1$
7		df-9	$⊢ 9 = 8 + 1$
8	7	oveq1i	$⊢ 9 + 1 = 8 + 1 + 1$
9		9p1e10	$⊢ 9 + 1 = 10$
10	6 8 9	3eqtr2i	$⊢ 8 + 2 = 10$