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 Th164:
  z <> x implies (Ex(z,G) = Ex(z,H)/(x,y) iff G = H/(x,y))
proof
  assume z <> x;
  then 'not' G = ('not' H)/(x,y) iff All(z,'not' G) = All(z,'not' H)/(x,y) by
Th159;
  hence thesis by Th156;
end;
