View source for Every bijection yields an inverse function

{{Stub page|grade=A*|msg=Flesh out with some details then demote to lower grade stub. Creating page largely to jog readers' memories. Not as a reference}}
==Statement==
Let {{M|X}} and {{M|Y}} be [[sets]] and suppose {{M|f:X\rightarrow Y}} is a [[map]] between them, and that it is a [[bijective]] map. Then there exists a unique function:
* {{M|f^{-1}:Y\rightarrow X}} such that {{M|1=f^{-1}(y)=x\iff f(x)=y}}
==Proof==
{{Requires proof|grade=E|msg=Easy proof.|easy=true}}
==References==
<references/>
{{Function terminology navbox|plain}}
{{Definition|Elementary Set Theory|Set Theory}}