theorem Th153:
  ex z1,z2 st (x1 '=' x2)/(y1,y2) = z1 '=' z2
proof
  x1 <> y1 & x2 <> y1 or x1 = y1 & x2 <> y1 or x1 <> y1 & x2 = y1 or x1 =
  y1 & x2 = y1;
  then consider z1,z2 such that
A1: x1 <> y1 & x2 <> y1 & z1 = x1 & z2 = x2 or x1 = y1 & x2 <> y1 & z1 =
  y2 & z2 = x2 or x1 <> y1 & x2 = y1 & z1 = x1 & z2 = y2 or x1 = y1 & x2 = y1 &
  z1 = y2 & z2 = y2;
  take z1,z2;
  thus thesis by A1,Th152;
end;
