Theorem add32i

Description: Commutative/associative law that swaps the last two terms in a triple sum. (Contributed by NM, 21-Jan-1997)

	Ref	Expression
Hypotheses	add.1	$$⊢A\in ℂ$$
	add.2	$$⊢B\in ℂ$$
	add.3	$$⊢C\in ℂ$$
Assertion	add32i	$$⊢A+B+C=A+C+B$$

Proof

Step	Hyp	Ref	Expression
1		add.1	$$⊢A\in ℂ$$
2		add.2	$$⊢B\in ℂ$$
3		add.3	$$⊢C\in ℂ$$
4		add32	$$⊢\left(A\in ℂ\wedge B\in ℂ\wedge C\in ℂ\right)\to A+B+C=A+C+B$$
5	1 2 3 4	mp3an	$$⊢A+B+C=A+C+B$$