Theorem rediv11d

Description: One-to-one relationship for division. (Contributed by SN, 9-Apr-2026)

	Ref	Expression
Hypotheses	rediv23d.a	$$⊢\phi \to A\in ℝ$$
	rediv23d.b	$$⊢\phi \to B\in ℝ$$
	rediv23d.c	$$⊢\phi \to C\in ℝ$$
	rediv23d.z	$$⊢\phi \to C\ne 0$$
Assertion	rediv11d	Could not format assertion : No typesetting found for |- ( ph -> ( ( A /R C ) = ( B /R C ) <-> A = B ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		rediv23d.a	$$⊢\phi \to A\in ℝ$$
2		rediv23d.b	$$⊢\phi \to B\in ℝ$$
3		rediv23d.c	$$⊢\phi \to C\in ℝ$$
4		rediv23d.z	$$⊢\phi \to C\ne 0$$
5	2 3 4	sn-redivcld	Could not format ( ph -> ( B /R C ) e. RR ) : No typesetting found for |- ( ph -> ( B /R C ) e. RR ) with typecode |-
6	1 5 3 4	redivmul2d	Could not format ( ph -> ( ( A /R C ) = ( B /R C ) <-> A = ( C x. ( B /R C ) ) ) ) : No typesetting found for |- ( ph -> ( ( A /R C ) = ( B /R C ) <-> A = ( C x. ( B /R C ) ) ) ) with typecode |-
7	2 3 4	redivcan2d	Could not format ( ph -> ( C x. ( B /R C ) ) = B ) : No typesetting found for |- ( ph -> ( C x. ( B /R C ) ) = B ) with typecode |-
8	7	eqeq2d	Could not format ( ph -> ( A = ( C x. ( B /R C ) ) <-> A = B ) ) : No typesetting found for |- ( ph -> ( A = ( C x. ( B /R C ) ) <-> A = B ) ) with typecode |-
9	6 8	bitrd	Could not format ( ph -> ( ( A /R C ) = ( B /R C ) <-> A = B ) ) : No typesetting found for |- ( ph -> ( ( A /R C ) = ( B /R C ) <-> A = B ) ) with typecode |-