reserve A,B,X,X1,Y,Y1,Y2,Z for set, a,x,y,z for object;
reserve P,R for Relation of X,Y;

theorem
  a in R implies ex x,y st a = [x,y] & x in X & y in Y
proof
  assume
A1: a in R;
  then consider x,y being object such that
A2: a = [x,y] by RELAT_1:def 1;
  x in X & y in Y by A1,A2,ZFMISC_1:87;
  hence thesis by A2;
end;
