theorem
  J |= p => q & not x in still_not-bound_in p implies J |= p => All(x,q)
proof
  assume that
A1: for v holds J,v |= p => q and
A2: not x in still_not-bound_in p;
  let u;
  now
    assume
A3: J,u |= p;
    now
      let w;
      assume for y st x<>y holds w.y = u.y;
      then
A4:   J,w |= p by A2,A3,Th28;
      J,w |= p => q by A1;
      hence J,w |= q by A4,Th24;
    end;
    hence J,u |= All(x,q) by Th29;
  end;
  hence thesis by Th24;
end;
