reserve a,b,c,d,x,y,z for object, X,Y,Z for set;
reserve R,S,T for Relation;
reserve F,G for Function;

theorem Th23:
  R |_2 field R = R
proof
  let x,y be object;
  thus [x,y] in R |_2 field R implies [x,y] in R by XBOOLE_0:def 4;
  assume
A1: [x,y] in R;
  then x in field R & y in field R by RELAT_1:15;
  then [x,y] in [:field R,field R:] by ZFMISC_1:87;
  hence thesis by A1,XBOOLE_0:def 4;
end;
