Theorem redivcli

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

	Ref	Expression
Hypotheses	redivcl.1	⊢ 𝐴 ∈ ℝ
	redivcl.2	⊢ 𝐵 ∈ ℝ
	redivcl.3	⊢ 𝐵 ≠ 0
Assertion	redivcli	⊢ ( 𝐴 / 𝐵 ) ∈ ℝ

Proof

Step	Hyp	Ref	Expression
1		redivcl.1	⊢ 𝐴 ∈ ℝ
2		redivcl.2	⊢ 𝐵 ∈ ℝ
3		redivcl.3	⊢ 𝐵 ≠ 0
4	1 2	redivclzi	⊢ ( 𝐵 ≠ 0 → ( 𝐴 / 𝐵 ) ∈ ℝ )
5	3 4	ax-mp	⊢ ( 𝐴 / 𝐵 ) ∈ ℝ