Is this known?

[Michael Barr <barr@math.mcgill.ca>]

In the course of certain studies on commutative rings, we needed the 
following result (to be sure, for ideals, not congruences):

Let \Csc be a regular category and $f:A\to B$ an epimorphism in
\Csc.  Suppose $E_1$ and $E_2$ are congruences on $B$ with $D_1$ and
$D_2$ their inverse images under $f\x f$.  If the induced $A/D_1\to
B/E_1$ is an isomorphism and $D_1\inc D_2$, then $E_1\inc E_2$

Michael


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