Theorem rerecclzi

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

	Ref	Expression
Hypothesis	redivcl.1	⊢ 𝐴 ∈ ℝ
Assertion	rerecclzi	⊢ ( 𝐴 ≠ 0 → ( 1 / 𝐴 ) ∈ ℝ )

Proof

Step	Hyp	Ref	Expression
1		redivcl.1	⊢ 𝐴 ∈ ℝ
2		rereccl	⊢ ( ( 𝐴 ∈ ℝ ∧ 𝐴 ≠ 0 ) → ( 1 / 𝐴 ) ∈ ℝ )
3	1 2	mpan	⊢ ( 𝐴 ≠ 0 → ( 1 / 𝐴 ) ∈ ℝ )