Theorem rediveq1d

Description: Equality in terms of unit ratio. (Contributed by SN, 2-Apr-2026)

	Ref	Expression
Hypotheses	redivcan2d.a	$$⊢\phi \to A\in ℝ$$
	redivcan2d.b	$$⊢\phi \to B\in ℝ$$
	redivcan2d.z	$$⊢\phi \to B\ne 0$$
Assertion	rediveq1d	Could not format assertion : No typesetting found for |- ( ph -> ( ( A /R B ) = 1 <-> A = B ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		redivcan2d.a	$$⊢\phi \to A\in ℝ$$
2		redivcan2d.b	$$⊢\phi \to B\in ℝ$$
3		redivcan2d.z	$$⊢\phi \to B\ne 0$$
4		1red	$$⊢\phi \to 1\in ℝ$$
5	1 4 2 3	redivmul2d	Could not format ( ph -> ( ( A /R B ) = 1 <-> A = ( B x. 1 ) ) ) : No typesetting found for |- ( ph -> ( ( A /R B ) = 1 <-> A = ( B x. 1 ) ) ) with typecode |-
6		ax-1rid	$$⊢B\in ℝ\to B\cdot 1=B$$
7	2 6	syl	$$⊢\phi \to B\cdot 1=B$$
8	7	eqeq2d	$$⊢\phi \to \left(A=B\cdot 1\leftrightarrow A=B\right)$$
9	5 8	bitrd	Could not format ( ph -> ( ( A /R B ) = 1 <-> A = B ) ) : No typesetting found for |- ( ph -> ( ( A /R B ) = 1 <-> A = B ) ) with typecode |-