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
  dom R c= X1 implies R is Relation of X1,Y
proof
A1: rng R c= Y by RELAT_1:def 19;
  assume dom R c= X1;
  then R c= [:dom R, rng R:] & [:dom R, rng R:] c= [:X1,Y:] by A1,RELAT_1:7
,ZFMISC_1:96;
  hence thesis by XBOOLE_1:1;
end;
