# 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