Theorem mul32i

Description: Commutative/associative law that swaps the last two factors in a triple product. (Contributed by NM, 11-May-1999)

	Ref	Expression
Hypotheses	mul.1	$$⊢A\in ℂ$$
	mul.2	$$⊢B\in ℂ$$
	mul.3	$$⊢C\in ℂ$$
Assertion	mul32i	$$⊢ABC=ACB$$

Proof

Step	Hyp	Ref	Expression
1		mul.1	$$⊢A\in ℂ$$
2		mul.2	$$⊢B\in ℂ$$
3		mul.3	$$⊢C\in ℂ$$
4		mul32	$$⊢\left(A\in ℂ\wedge B\in ℂ\wedge C\in ℂ\right)\to ABC=ACB$$
5	1 2 3 4	mp3an	$$⊢ABC=ACB$$