Inverse Mapping is Unique

Theorem
Let $$f: S \to T$$ be a mapping.

If $$f$$ has an inverse mapping, then that inverse mapping is unique.

Proof
Suppose $$g$$ and $$h$$ are both inverse mappings of $$f$$.

Then by the definition of inverse mapping, we have:

$$ $$

and:

$$ $$

So:

$$ $$ $$ $$ $$

So $$g = h$$ and the inverse is unique.