Theorem remulcld

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

	Ref	Expression
Hypotheses	recnd.1	$$⊢\phi \to A\in ℝ$$
	readdcld.2	$$⊢\phi \to B\in ℝ$$
Assertion	remulcld	$$⊢\phi \to AB\in ℝ$$

Proof

Step	Hyp	Ref	Expression
1		recnd.1	$$⊢\phi \to A\in ℝ$$
2		readdcld.2	$$⊢\phi \to B\in ℝ$$
3		remulcl	$$⊢\left(A\in ℝ\wedge B\in ℝ\right)\to AB\in ℝ$$
4	1 2 3	syl2anc	$$⊢\phi \to AB\in ℝ$$