reserve A,X,X1,X2,Y,Y1,Y2 for set, a,b,c,d,x,y,z for object;
reserve P,P1,P2,Q,R,S for Relation;

theorem Th62:
  dom R c= X implies R|X = R
proof
  assume dom R c= X; then
A1: [:dom R,rng R:] c= [:X,rng R:] by ZFMISC_1:95;
  R c= [:dom R,rng R:] & R|X = R /\ [:X,rng R:] by Th1,Th61;
  hence thesis by A1,XBOOLE_1:1,28;
end;
