Theorem sn-rediv1d

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

	Ref	Expression
Hypothesis	sn-rediv1d.a	$$⊢\phi \to A\in ℝ$$
Assertion	sn-rediv1d	$$⊢\phi \to A{/}_{ℝ}1=A$$

Proof

Step	Hyp	Ref	Expression
1		sn-rediv1d.a	$$⊢\phi \to A\in ℝ$$
2		remullid	$$⊢A\in ℝ\to 1A=A$$
3	1 2	syl	$$⊢\phi \to 1A=A$$
4		1red	$$⊢\phi \to 1\in ℝ$$
5		ax-1ne0	$$⊢1\ne 0$$
6	5	a1i	$$⊢\phi \to 1\ne 0$$
7	1 1 4 6	redivmuld	$$⊢\phi \to \left(A{/}_{ℝ}1=A\leftrightarrow 1A=A\right)$$
8	3 7	mpbird	$$⊢\phi \to A{/}_{ℝ}1=A$$