reserve p,q,x,x1,x2,y,y1,y2,z,z1,z2 for set;
reserve A,B,V,X,X1,X2,Y,Y1,Y2,Z for set;
reserve C,C1,C2,D,D1,D2 for non empty set;

theorem Th1:
  A c= Y implies id A = (id Y)|A
proof
  assume A c= Y;
  hence id A = id(Y /\ A) by XBOOLE_1:28
    .= (id Y)*(id A) by FUNCT_1:22
    .= (id Y)|A by RELAT_1:65;
end;
