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
  M |= Ex(x,H) iff for v ex m st M,v/(x,m) |= H
proof
  thus M |= Ex(x,H) implies for v ex m st M,v/(x,m) |= H
  by Th73;
  assume
A1: for v ex m st M,v/(x,m) |= H;
  let v;
  ex m st M,v/(x,m) |= H by A1;
  hence thesis by Th73;
end;
