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;
