Theorem rerecid2d

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	rerecid2d	$$⊢\phi \to \left(1{/}_{ℝ}A\right)A=1$$

Proof

Step	Hyp	Ref	Expression
1		sn-rereccld.a	$$⊢\phi \to A\in ℝ$$
2		sn-rereccld.z	$$⊢\phi \to A\ne 0$$
3	1 2	sn-rereccld	$$⊢\phi \to 1{/}_{ℝ}A\in ℝ$$
4	1 2	rerecidd	$$⊢\phi \to A\left(1{/}_{ℝ}A\right)=1$$
5	1 3 4	remulinvcom	$$⊢\phi \to \left(1{/}_{ℝ}A\right)A=1$$