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	$$⊢1+2=3$$