discrete mathematics – Proving $aequiv b pmod m$ if $a bmod m = bbmod m$

I want to prove that for integers $a, b$ and positive integers $m$, that $a equiv bpmod m$ iff $a bmod m = bbmod m$

I’m on my tablet currently so I cannot type up my latex well. But I’ve been trying to do a direct proof using the fact that $b=mq+r$. I also tried using propositional logic, since this is a biconditional I tried proving the implications in both directions, but I’m still getting confused