theorem Th38:
  {a,b}"" = {a",b"}
proof
  let z;
  hereby
    assume z in {a,b}"";
    then consider c such that
A1: z = c" and
A2: c in {a,b};
    c = a or c = b by A2,TARSKI:def 2;
    hence z in {a",b"} by A1,TARSKI:def 2;
  end;
A3: a in {a,b} & b in {a,b} by TARSKI:def 2;
  assume z in {a",b"};
  then
A4: z = a" or z = b" by TARSKI:def 2;
  thus thesis by A4,A3;
end;
