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Metamath Proof Explorer

Theorem 4p3e7

Description: 4 + 3 = 7. (Contributed by NM, 11-May-2004)

		Ref	Expression
	Assertion	4p3e7	$⊢ 4 + 3 = 7$

Proof

Step	Hyp	Ref	Expression
1		df-3	$⊢ 3 = 2 + 1$
2	1	oveq2i	$⊢ 4 + 3 = 4 + 2 + 1$
3		4cn	$⊢ 4 \in ℂ$
4		2cn	$⊢ 2 \in ℂ$
5		ax-1cn	$⊢ 1 \in ℂ$
6	3 4 5	addassi	$⊢ 4 + 2 + 1 = 4 + 2 + 1$
7	2 6	eqtr4i	$⊢ 4 + 3 = 4 + 2 + 1$
8		df-7	$⊢ 7 = 6 + 1$
9		4p2e6	$⊢ 4 + 2 = 6$
10	9	oveq1i	$⊢ 4 + 2 + 1 = 6 + 1$
11	8 10	eqtr4i	$⊢ 7 = 4 + 2 + 1$
12	7 11	eqtr4i	$⊢ 4 + 3 = 7$