X, card X are_equipotent by CARD_1:def 2;
then consider f being Function such that
A1: f is one-to-one and
A2: dom f = X and
A3: rng f = card X by WELLORD2:def 4;
reconsider f = f as Function of X,(card X) by A2, A3, FUNCT_2:2;
take f ; :: thesis: ( f is one-to-one & f is onto )
thus f is one-to-one by A1; :: thesis: f is onto
thus rng f = card X by A3; :: according to FUNCT_2:def 3 :: thesis: verum