reserve Al for QC-alphabet;
reserve b,c,d for set,
  X,Y for Subset of CQC-WFF(Al),
  i,j,k,m,n for Nat,
  p,p1,q,r,s,s1 for Element of CQC-WFF(Al),
  x,x1,x2,y,y1 for bound_QC-variable of Al,
  A for non empty set,
  J for interpretation of Al, A,
  v for Element of Valuations_in(Al,A),
  f1,f2 for FinSequence of CQC-WFF(Al),
  CX,CY,CZ for Consistent Subset of CQC-WFF(Al),
  JH for Henkin_interpretation of CX,
  a for Element of A,
  t,u for QC-symbol of Al;

theorem
  (CX is negation_faithful & CX is with_examples implies
  (JH,valH(Al) |= p iff CX |- p)) &
  (CX is negation_faithful & CX is with_examples implies
  (JH,valH(Al) |= q iff CX |- q)) implies
  (CX is negation_faithful & CX is with_examples
  implies (JH,valH(Al) |= p '&' q iff CX |- p '&' q)) by Th6,VALUAT_1:18;
