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 Th163:
  G1 <=> G2 = (H1 <=> H2)/(x,y) iff G1 = H1/(x,y) & G2 = H2/(x,y)
proof
  G1 <=> G2 = (H1 <=> H2)/(x,y) iff G1 => G2 = (H1 => H2)/(x,y) & G2 => G1
  = (H2 => H1)/(x,y) by Th158;
  hence thesis by Th162;
end;
