theorem Th17:
  for p holds (CX is negation_faithful & CX is with_examples
  implies (JH,valH(Al) |= p iff CX |- p))
proof
  defpred P[Element of CQC-WFF(Al)] means
  CX is negation_faithful & CX is with_examples
  implies (JH,valH(Al) |= $1 iff CX |- $1);
A1: for p st QuantNbr(p) <= 0 holds P[p] by Th8;
A2: for k st for p st QuantNbr(p) <= k holds P[p] holds
  for p st QuantNbr(p) <= k+1 holds P[p] by Th16;
  thus for p holds P[p] from SUBSTUT2:sch 2(A1,A2);
end;
