How to write this separately $ a = b \equiv c = 0\pmod f $?

Question

I would like to know if I could write this $$ a = b \equiv c = 0 \pmod f $$

without the "=" and "$\equiv$" in the same line, because my Prof doesn't like it.

This is my solution:

Let $c=0$ and $a = b$ than

$$ a \equiv c \pmod f .$$

Can I write it like that, without loosing something on the way?

If you have a better idea, please let me know.

Answer 1

Your notation is fine, but I suggest to add a short explanation: $$a=b\equiv c=d \pmod m\implies a\equiv d\pmod m$$ because the (modulo $m$) relation is reflexive and transitive.