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 Th35:
  x in dom p & p.x = TRUE & x in dom q & q.x = FALSE implies
   PP_imp(p,q).x = FALSE
  proof
    assume that
A1: x in dom p and
A2: p.x = TRUE and
A3: x in dom q and
A4: q.x = FALSE;
A5: dom PP_not(p) = dom p by Def2;
    PP_not(p).x = FALSE by A1,A2,Def2;
    hence thesis by A1,A3,A4,A5,Def4;
  end;
