Theorem redivclzi

Description: Closure law for division of reals. (Contributed by NM, 9-May-1999)

	Ref	Expression
Hypotheses	redivcl.1	$$⊢A\in ℝ$$
	redivcl.2	$$⊢B\in ℝ$$
Assertion	redivclzi	$$⊢B\ne 0\to \frac{A}{B}\in ℝ$$

Proof

Step	Hyp	Ref	Expression
1		redivcl.1	$$⊢A\in ℝ$$
2		redivcl.2	$$⊢B\in ℝ$$
3		redivcl	$$⊢\left(A\in ℝ\wedge B\in ℝ\wedge B\ne 0\right)\to \frac{A}{B}\in ℝ$$
4	1 2 3	mp3an12	$$⊢B\ne 0\to \frac{A}{B}\in ℝ$$