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Homework Statement
Let m be a positive integer. Show that a mod m = b mod m if [itex]a\,\equiv\,b\left(mod\,m\right)[/itex].
Homework Equations
Congruency - [tex]a\,\equiv\,b\left(mod\,m\right)[/tex]
a is congruent to b modulo m.
The Attempt at a Solution
I really, really, really suck at proofs. But here is what I tried.
[tex]a\,\equiv\,b\left(mod\,m\right)\,\longrightarrow\,a\,mod\,m\,\equiv\,\left[b\left(mod\,m\right)\right]\,\left(mod\,m\right)[/tex]
I have no idea how to prove anything about this stuff. Please help!!!