reserve X,Y,Z,x,y,z for set;
reserve T,R for Tolerance of X;

theorem Th15:
  for x,y st [x,y] in T holds {x,y} is TolSet of T
proof
  let x,y;
  assume
A1: [x,y] in T;
  then
A2: x in X & y in X by ZFMISC_1:87;
  for a,b being set st a in {x,y} & b in {x,y} holds [a,b] in T
  proof
    let a,b be set;
    assume that
A3: a in {x,y} and
A4: b in {x,y};
A5: b = x or b = y by A4,TARSKI:def 2;
    a = x or a = y by A3,TARSKI:def 2;
    hence thesis by A1,A2,A5,Th7,EQREL_1:6;
  end;
  hence thesis by Def1;
end;
