Theorem sn-redividd

Description: A number divided by itself is 1. (Contributed by SN, 2-Apr-2026)

	Ref	Expression
Hypotheses	sn-rediv0d.a	$$⊢\phi \to A\in ℝ$$
	sn-rediv0d.z	$$⊢\phi \to A\ne 0$$
Assertion	sn-redividd	$$⊢\phi \to A{/}_{ℝ}A=1$$

Proof

Step	Hyp	Ref	Expression
1		sn-rediv0d.a	$$⊢\phi \to A\in ℝ$$
2		sn-rediv0d.z	$$⊢\phi \to A\ne 0$$
3		eqidd	$$⊢\phi \to A=A$$
4	1 1 2	rediveq1d	$$⊢\phi \to \left(A{/}_{ℝ}A=1\leftrightarrow A=A\right)$$
5	3 4	mpbird	$$⊢\phi \to A{/}_{ℝ}A=1$$