| context | $X,Y$ |
| definiendum | $ f\in\text{PartialFunction}(X,Y) $ |
| context | $ f \in \text{Rel}(X,Y) $ |
| postulate | $ \langle x,a\rangle\in f \land \langle x,b\rangle\in f \Rightarrow a=b $ |
The definition can be written as
$\{\langle x,a\rangle,\langle x,b\rangle\}\subseteq f \Rightarrow a=b.$
It says that each argument $x$ for the function can result in only one value. (functionality)
Wikipedia: Partial function