theorem
  M,v |= Ex(x,H) iff M,v/(x,m) |= Ex(x,H)
proof
A1: for v,m st M,v |= Ex(x,H) holds M,v/(x,m) |= Ex(x,H)
  proof
    let v,m;
    assume M,v |= Ex(x,H);
    then consider m9 such that
A2: M,v/(x,m9) |= H by Th73;
    (v/(x,m))/(x,m9) = v/(x,m9) by FUNCT_7:34;
    hence thesis by A2,Th73;
  end;
  (v/(x,m))/(x,v.x) = v/(x,v.x) by FUNCT_7:34
    .= v by FUNCT_7:35;
  hence thesis by A1;
end;
