 reserve x,y,z,t for object,X,Y,Z,W for set;
 reserve R,S,T for Relation;

theorem Th15:
  X c= Y implies id X c= id Y
proof
  assume X c= Y;
  then X \/ Y = Y by XBOOLE_1:12;
  then id(X) \/ id Y = id Y by Th14;
  hence thesis by XBOOLE_1:7;
end;
