Theorem sn-rereccld

Description: Closure law for reciprocal. (Contributed by SN, 25-Nov-2025)

	Ref	Expression
Hypotheses	sn-rereccld.a	$$⊢\phi \to A\in ℝ$$
	sn-rereccld.z	$$⊢\phi \to A\ne 0$$
Assertion	sn-rereccld	$$⊢\phi \to 1{/}_{ℝ}A\in ℝ$$

Proof

Step	Hyp	Ref	Expression
1		sn-rereccld.a	$$⊢\phi \to A\in ℝ$$
2		sn-rereccld.z	$$⊢\phi \to A\ne 0$$
3		1red	$$⊢\phi \to 1\in ℝ$$
4	3 1 2	sn-redivcld	$$⊢\phi \to 1{/}_{ℝ}A\in ℝ$$