let X, Y be set ; :: thesis: for f being Function of X,Y st ( Y = {} implies X = {} ) holds
TotFuncs <:f,X,Y:> = {f}
let f be Function of X,Y; :: thesis: ( ( Y = {} implies X = {} ) implies TotFuncs <:f,X,Y:> = {f} )
assume ( Y = {} implies X = {} ) ; :: thesis: TotFuncs <:f,X,Y:> = {f}
then ( <:f,X,Y:> is total & <:f,X,Y:> = f ) by PARTFUN1:87;
hence TotFuncs <:f,X,Y:> = {f} by PARTFUN1:174; :: thesis: verum