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

Metamath Proof Explorer

Theorem 1p2e3

Description: 1 + 2 = 3. For a shorter proof using addcomli , see 1p2e3ALT . (Contributed by David A. Wheeler, 8-Dec-2018) Reduce dependencies on axioms. (Revised by Steven Nguyen, 12-Dec-2022)

		Ref	Expression
	Assertion	1p2e3	$⊢ 1 + 2 = 3$

Proof

Step	Hyp	Ref	Expression
1		df-2	$⊢ 2 = 1 + 1$
2	1	oveq2i	$⊢ 1 + 2 = 1 + 1 + 1$
3		ax-1cn	$⊢ 1 \in ℂ$
4	3 3 3	addassi	$⊢ 1 + 1 + 1 = 1 + 1 + 1$
5		1p1e2	$⊢ 1 + 1 = 2$
6	5	oveq1i	$⊢ 1 + 1 + 1 = 2 + 1$
7		2p1e3	$⊢ 2 + 1 = 3$
8	6 7	eqtri	$⊢ 1 + 1 + 1 = 3$
9	2 4 8	3eqtr2i	$⊢ 1 + 2 = 3$