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Metamath Proof Explorer

Theorem 3p3e6

Description: 3 + 3 = 6. (Contributed by NM, 11-May-2004)

		Ref	Expression
	Assertion	3p3e6	$⊢ 3 + 3 = 6$

Proof

Step	Hyp	Ref	Expression
1		df-3	$⊢ 3 = 2 + 1$
2	1	oveq2i	$⊢ 3 + 3 = 3 + 2 + 1$
3		3cn	$⊢ 3 \in ℂ$
4		2cn	$⊢ 2 \in ℂ$
5		ax-1cn	$⊢ 1 \in ℂ$
6	3 4 5	addassi	$⊢ 3 + 2 + 1 = 3 + 2 + 1$
7	2 6	eqtr4i	$⊢ 3 + 3 = 3 + 2 + 1$
8		df-6	$⊢ 6 = 5 + 1$
9		3p2e5	$⊢ 3 + 2 = 5$
10	9	oveq1i	$⊢ 3 + 2 + 1 = 5 + 1$
11	8 10	eqtr4i	$⊢ 6 = 3 + 2 + 1$
12	7 11	eqtr4i	$⊢ 3 + 3 = 6$