let X be set ; :: thesis: for f being Function of X,X holds
( f is one-to-one iff for x1, x2 being set st x1 in X & x2 in X & f . x1 = f . x2 holds
x1 = x2 )
let f be Function of X,X; :: thesis: ( f is one-to-one iff for x1, x2 being set st x1 in X & x2 in X & f . x1 = f . x2 holds
x1 = x2 )
dom f = X by Th67;
hence ( f is one-to-one iff for x1, x2 being set st x1 in X & x2 in X & f . x1 = f . x2 holds
x1 = x2 ) by FUNCT_1:def 8; :: thesis: verum