consider A being AbGroup;
take <*A*> ; :: thesis: ( not <*A*> is empty & <*A*> is AbGroup-yielding )
thus not <*A*> is empty ; :: thesis: <*A*> is AbGroup-yielding
let x be set ; :: according to PRVECT_1:def 11 :: thesis: ( x in rng <*A*> implies x is AbGroup )
assume A1: ( x in rng <*A*> & x is not AbGroup ) ; :: thesis: contradiction
then x in {A} by FINSEQ_1:55;
hence contradiction by A1, TARSKI:def 1; :: thesis: verum