Theorem mulassd

Description: Associative law for multiplication. (Contributed by Mario Carneiro, 27-May-2016)

	Ref	Expression
Hypotheses	addcld.1	$$⊢\phi \to A\in ℂ$$
	addcld.2	$$⊢\phi \to B\in ℂ$$
	addassd.3	$$⊢\phi \to C\in ℂ$$
Assertion	mulassd	$$⊢\phi \to ABC=ABC$$

Proof

Step	Hyp	Ref	Expression
1		addcld.1	$$⊢\phi \to A\in ℂ$$
2		addcld.2	$$⊢\phi \to B\in ℂ$$
3		addassd.3	$$⊢\phi \to C\in ℂ$$
4		mulass	$$⊢\left(A\in ℂ\wedge B\in ℂ\wedge C\in ℂ\right)\to ABC=ABC$$
5	1 2 3 4	syl3anc	$$⊢\phi \to ABC=ABC$$