Theorem rerpdivcld

Description: Closure law for division of a real by a positive real. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypotheses	rpgecld.1	$$⊢\phi \to A\in ℝ$$
	rpgecld.2	$$⊢\phi \to B\in {ℝ}^{+}$$
Assertion	rerpdivcld	$$⊢\phi \to \frac{A}{B}\in ℝ$$

Proof

Step	Hyp	Ref	Expression
1		rpgecld.1	$$⊢\phi \to A\in ℝ$$
2		rpgecld.2	$$⊢\phi \to B\in {ℝ}^{+}$$
3		rerpdivcl	$$⊢\left(A\in ℝ\wedge B\in {ℝ}^{+}\right)\to \frac{A}{B}\in ℝ$$
4	1 2 3	syl2anc	$$⊢\phi \to \frac{A}{B}\in ℝ$$