reserve x for object;
reserve D for set;
reserve p for PartialPredicate of D;
reserve D for non empty set;
reserve p,q,r for PartialPredicate of D;

theorem
  PP_or(PP_imp(p,r),PP_imp(q,r)) = PP_imp(PP_and(p,q),r)
  proof
    PP_or(PP_or(r,PP_not(p)),PP_or(r,PP_not(q)))
    = PP_or(PP_or(r,PP_not(p)),PP_not(q)) by Th15;
    hence thesis by Th14;
  end;
