
theorem Th77:
  for x,y being set, z being object holds [z,2] in x U+ y iff z in y
proof
  let x,y be set, z be object;
  x U+ y = [:x,{1}:] \/ [:y,{2}:] by Th73;
  then
  [z,2] in x U+ y iff [z,2] in [:x,{1}:] & 1 <> 2 or [z,2] in [:y,{2}:] by
XBOOLE_0:def 3;
  hence thesis by ZFMISC_1:106;
end;
