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The definition
Let f be a binary relation. f is a partial function if every element of its domain is in relation to at most one element of its range.as well as the definition
A partial function is a binary relation where every element of the domain is in relation to at most one element of the range.are to be read as the definition of a unary predicate
f is a partial function : <=>
f is a binary relation /\
forall x, y_0, y_1: (<x, y_0> in f /\ <x, y_1> in f) => y_0 = y_1.