Theorem mulassi

Description: Associative law for multiplication. (Contributed by NM, 23-Nov-1994)

	Ref	Expression
Hypotheses	axi.1	$$⊢A\in ℂ$$
	axi.2	$$⊢B\in ℂ$$
	axi.3	$$⊢C\in ℂ$$
Assertion	mulassi	$$⊢ABC=ABC$$

Proof

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