Theorem remulcld

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

	Ref	Expression
Hypotheses	recnd.1	|- ( ph -> A e. RR )
	readdcld.2	|- ( ph -> B e. RR )
Assertion	remulcld	|- ( ph -> ( A x. B ) e. RR )

Proof

Step	Hyp	Ref	Expression
1		recnd.1	|- ( ph -> A e. RR )
2		readdcld.2	|- ( ph -> B e. RR )
3		remulcl	|- ( ( A e. RR /\ B e. RR ) -> ( A x. B ) e. RR )
4	1 2 3	syl2anc	|- ( ph -> ( A x. B ) e. RR )