set A = the AbGroup;
take <* the AbGroup*> ; :: thesis: ( not <* the AbGroup*> is empty & <* the AbGroup*> is AbGroup-yielding )
thus not <* the AbGroup*> is empty ; :: thesis: <* the AbGroup*> is AbGroup-yielding
let x be set ; :: according to PRVECT_1:def 10 :: thesis: ( x in rng <* the AbGroup*> implies x is AbGroup )
assume that
A1: x in rng <* the AbGroup*> and
A2: x is not AbGroup ; :: thesis: contradiction
x in { the AbGroup} by A1, FINSEQ_1:38;
hence contradiction by A2, TARSKI:def 1; :: thesis: verum