let X, Y be set ; :: thesis: for f being Function of X,Y st Y <> {} & ex g being Function of Y,X st g * f = id X holds
f is one-to-one
let f be Function of X,Y; :: thesis: ( Y <> {} & ex g being Function of Y,X st g * f = id X implies f is one-to-one )
assume A1: Y <> {} ; :: thesis: ( for g being Function of Y,X holds not g * f = id X or f is one-to-one )
given g being Function of Y,X such that A2: g * f = id X ; :: thesis: f is one-to-one
dom f = X by A1, Def1;
hence f is one-to-one by A2, FUNCT_1:53; :: thesis: verum