Theorem mulcld

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

	Ref	Expression
Hypotheses	addcld.1	$$⊢\phi \to A\in ℂ$$
	addcld.2	$$⊢\phi \to B\in ℂ$$
Assertion	mulcld	$$⊢\phi \to AB\in ℂ$$

Proof

Step	Hyp	Ref	Expression
1		addcld.1	$$⊢\phi \to A\in ℂ$$
2		addcld.2	$$⊢\phi \to B\in ℂ$$
3		mulcl	$$⊢\left(A\in ℂ\wedge B\in ℂ\right)\to AB\in ℂ$$
4	1 2 3	syl2anc	$$⊢\phi \to AB\in ℂ$$