
theorem Th74:
  for x being set holds x U+ {} = [:x,{1}:] & {} U+ x = [:x,{2}:]
proof
  let x be set;
  thus x U+ {} = [:x,{1}:] \/ [:{},{2}:] by Th73
    .= [:x,{1}:] \/ {} by ZFMISC_1:90
    .= [:x,{1}:];
  thus {} U+ x = [:{},{1}:] \/ [:x,{2}:] by Th73
    .= {} \/ [:x,{2}:] by ZFMISC_1:90
    .= [:x,{2}:];
end;
