Theorem rereccli

Description: Closure law for reciprocal. (Contributed by NM, 30-Apr-2005)

	Ref	Expression
Hypotheses	redivcl.1	⊢ 𝐴 ∈ ℝ
	rereccl.2	⊢ 𝐴 ≠ 0
Assertion	rereccli	⊢ ( 1 / 𝐴 ) ∈ ℝ

Proof

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