let A, a, b be set ; :: thesis: ( <*a,b*> in 2 -tuples_on A implies ( a in A & b in A ) )
assume <*a,b*> in 2 -tuples_on A ; :: thesis: ( a in A & b in A )
then A1: ex a9, b9 being set st
( a9 in A & b9 in A & <*a,b*> = <*a9,b9*> ) by Th157;
( <*a,b*> . 1 = a & <*a,b*> . 2 = b ) by FINSEQ_1:44;
hence ( a in A & b in A ) by A1, FINSEQ_1:44; :: thesis: verum