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;
reserve L for PATH of q,p,
  F1,F3 for QC-formula of Al,
  a for set;

theorem Th21:
  p in X implies X |- p
proof
  assume
A1: p in X;
  now
    let a be object;
    assume a in rng <*p*>;
    then a in {p} by FINSEQ_1:38;
    hence a in X by A1,TARSKI:def 1;
  end;
  then
A2: rng <*p*> c= X;
  |- <*>CQC-WFF(Al)^<*p*>^<*p*> by CALCUL_2:21;
  then |- <*p*>^<*p*> by FINSEQ_1:34;
  hence thesis by A2,HENMODEL:def 1;
end;
