This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem 5p3e8

Description: 5 + 3 = 8. (Contributed by NM, 11-May-2004)

		Ref	Expression
	Assertion	5p3e8	$⊢ 5 + 3 = 8$

Proof

Step	Hyp	Ref	Expression
1		df-3	$⊢ 3 = 2 + 1$
2	1	oveq2i	$⊢ 5 + 3 = 5 + 2 + 1$
3		5cn	$⊢ 5 \in ℂ$
4		2cn	$⊢ 2 \in ℂ$
5		ax-1cn	$⊢ 1 \in ℂ$
6	3 4 5	addassi	$⊢ 5 + 2 + 1 = 5 + 2 + 1$
7	2 6	eqtr4i	$⊢ 5 + 3 = 5 + 2 + 1$
8		df-8	$⊢ 8 = 7 + 1$
9		5p2e7	$⊢ 5 + 2 = 7$
10	9	oveq1i	$⊢ 5 + 2 + 1 = 7 + 1$
11	8 10	eqtr4i	$⊢ 8 = 5 + 2 + 1$
12	7 11	eqtr4i	$⊢ 5 + 3 = 8$