Theorem addcomi

Description: Addition is commutative. Based on ideas by Eric Schmidt. (Contributed by Scott Fenton, 3-Jan-2013)

	Ref	Expression
Hypotheses	mul.1	$$⊢A\in ℂ$$
	mul.2	$$⊢B\in ℂ$$
Assertion	addcomi	$$⊢A+B=B+A$$

Proof

Step	Hyp	Ref	Expression
1		mul.1	$$⊢A\in ℂ$$
2		mul.2	$$⊢B\in ℂ$$
3		addcom	$$⊢\left(A\in ℂ\wedge B\in ℂ\right)\to A+B=B+A$$
4	1 2 3	mp2an	$$⊢A+B=B+A$$