Theorem remulcli

Description: Closure law for multiplication of reals. (Contributed by NM, 17-Jan-1997)

	Ref	Expression
Hypotheses	recni.1	$$⊢A\in ℝ$$
	axri.2	$$⊢B\in ℝ$$
Assertion	remulcli	$$⊢AB\in ℝ$$

Proof

Step	Hyp	Ref	Expression
1		recni.1	$$⊢A\in ℝ$$
2		axri.2	$$⊢B\in ℝ$$
3		remulcl	$$⊢\left(A\in ℝ\wedge B\in ℝ\right)\to AB\in ℝ$$
4	1 2 3	mp2an	$$⊢AB\in ℝ$$