thus A --> z is Function-like :: thesis: A --> z is Relation-like

proof

let x, y1, y2 be object ; :: according to FUNCT_1:def 1 :: thesis: ( not [x,y1] in A --> z or not [x,y2] in A --> z or y1 = y2 )
assume that
A1: [x,y1] in A --> z and
A2: [x,y2] in A --> z ; :: thesis: y1 = y2
y1 in {z} by A1, ZFMISC_1:87;
then A3: y1 = z by TARSKI:def 1;
y2 in {z} by A2, ZFMISC_1:87;
hence y1 = y2 by A3, TARSKI:def 1; :: thesis: verum

end;

thus for x being object st x in A --> z holds
ex y1, y2 being object st [y1,y2] = x by RELAT_1:def 1; :: according to RELAT_1:def 1 :: thesis: verum