theorem Th72:
  M,v |= All(x,H) iff M,v/(x,m) |= All(x,H)
proof
A1: for v,m st M,v |= All(x,H) holds M,v/(x,m) |= All(x,H)
  proof
    let v,m such that
A2: M,v |= All(x,H);
    now
      let m9;
      (v/(x,m))/(x,m9) = v/(x,m9) by FUNCT_7:34;
      hence M,(v/(x,m))/(x,m9) |= H by A2,Th71;
    end;
    hence thesis by Th71;
  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;
