theorem
  p is valid & p => q is valid implies q is valid
proof
A1: TAUT(Al) is being_a_theory by Th11;
  assume p is valid & p => q is valid;
  then  p in TAUT(Al) & p => q in TAUT(Al);
  then  q in TAUT(Al) by A1;
  hence thesis;
end;
