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 Th37:
  id(field R) is_isomorphism_of R,R
proof
A1: now
    let a,b;
    thus [a,b] in R implies a in field R & b in field R & [id(field R).a,id(
    field R).b] in R
    proof
      assume
A2:   [a,b] in R;
      hence
A3:   a in field R & b in field R by RELAT_1:15;
      then id(field R).a = a by FUNCT_1:18;
      hence thesis by A2,A3,FUNCT_1:18;
    end;
    assume that
A4: a in field R and
A5: b in field R & [id(field R).a,id(field R).b] in R;
    id(field R).a = a by A4,FUNCT_1:18;
    hence [a,b] in R by A5,FUNCT_1:18;
  end;
  thus thesis by A1;
end;
