Theorem rerecidd

Description: Multiplication of a number and its 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	rerecidd	$$⊢\phi \to A\left(1{/}_{ℝ}A\right)=1$$

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	redivcan2d	$$⊢\phi \to A\left(1{/}_{ℝ}A\right)=1$$