reserve p,p1,p2,q,r,F,G,G1,G2,H,H1,H2 for ZF-formula,
  x,x1,x2,y,y1,y2,z,z1,z2,s,t for Variable,
  a,X for set;
reserve M for non empty set,
  m,m9 for Element of M,
  v,v9 for Function of VAR,M;
reserve i,j for Element of NAT;

theorem Th155:
  ex z1,z2 st (x1 'in' x2)/(y1,y2) = z1 'in' 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,Th154;
end;
