Congruence by Divisor of Modulus

Theorem
Let $$a \equiv b \pmod n$$.

Let $$m \in \Z, m > 0$$ such that $$m \backslash n$$.

Then $$a \equiv b \pmod m$$.

Proof
We have $$m \backslash n$$, so by definition of divides, $$n = k_1 m$$ for some $$k_1 \in \Z$$.

Thus:

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