Metamath Proof Explorer


Theorem redivmul2d

Description: Relationship between division and multiplication. (Contributed by SN, 2-Apr-2026)

Ref Expression
Hypotheses redivmuld.a φ A
redivmuld.b φ B
redivmuld.c φ C
redivmuld.z φ C 0
Assertion redivmul2d Could not format assertion : No typesetting found for |- ( ph -> ( ( A /R C ) = B <-> A = ( C x. B ) ) ) with typecode |-

Proof

Step Hyp Ref Expression
1 redivmuld.a φ A
2 redivmuld.b φ B
3 redivmuld.c φ C
4 redivmuld.z φ C 0
5 1 2 3 4 redivmuld Could not format ( ph -> ( ( A /R C ) = B <-> ( C x. B ) = A ) ) : No typesetting found for |- ( ph -> ( ( A /R C ) = B <-> ( C x. B ) = A ) ) with typecode |-
6 eqcom C B = A A = C B
7 5 6 bitrdi Could not format ( ph -> ( ( A /R C ) = B <-> A = ( C x. B ) ) ) : No typesetting found for |- ( ph -> ( ( A /R C ) = B <-> A = ( C x. B ) ) ) with typecode |-