Theorem mulcli

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

	Ref	Expression
Hypotheses	axi.1	$$⊢A\in ℂ$$
	axi.2	$$⊢B\in ℂ$$
Assertion	mulcli	$$⊢AB\in ℂ$$

Proof

Step	Hyp	Ref	Expression
1		axi.1	$$⊢A\in ℂ$$
2		axi.2	$$⊢B\in ℂ$$
3		mulcl	$$⊢\left(A\in ℂ\wedge B\in ℂ\right)\to AB\in ℂ$$
4	1 2 3	mp2an	$$⊢AB\in ℂ$$