Theorem mulcld

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

	Ref	Expression
Hypotheses	addcld.1	|- ( ph -> A e. CC )
	addcld.2	|- ( ph -> B e. CC )
Assertion	mulcld	|- ( ph -> ( A x. B ) e. CC )

Proof

Step	Hyp	Ref	Expression
1		addcld.1	|- ( ph -> A e. CC )
2		addcld.2	|- ( ph -> B e. CC )
3		mulcl	|- ( ( A e. CC /\ B e. CC ) -> ( A x. B ) e. CC )
4	1 2 3	syl2anc	|- ( ph -> ( A x. B ) e. CC )