
theorem Th1: :: set00:
for X, Y, x being set st not x in X holds X \ (Y \/ {x}) = X \ Y
proof
  let X, Y, x be set;
  assume not x in X;
   then A1: not x in X \ Y;
  thus X \ (Y \/ {x}) = (X \ Y) \ {x} by XBOOLE_1:41
   .= X \ Y by A1,ZFMISC_1:57;
end;
