theorem Th80:
  Subformulae x '=' y = { x '=' y }
proof
  now
    let a be object;
    thus a in Subformulae x '=' y implies a in { x '=' y }
    proof
      assume a in Subformulae x '=' y;
      then consider F such that
A1:   F = a and
A2:   F is_subformula_of x '=' y by Def42;
      F = x '=' y by A2,Th76;
      hence thesis by A1,TARSKI:def 1;
    end;
    assume a in { x '=' y };
    then
A3: a = x '=' y by TARSKI:def 1;
    x '=' y is_subformula_of x '=' y by Th59;
    hence a in Subformulae x '=' y by A3,Def42;
  end;
  hence thesis by TARSKI:2;
end;
