reserve Al for QC-alphabet;
reserve i,j,n,k,l for Nat;
reserve a for set;
reserve T,S,X,Y for Subset of CQC-WFF(Al);
reserve p,q,r,t,F,H,G for Element of CQC-WFF(Al);
reserve s for QC-formula of Al;
reserve x,y for bound_QC-variable of Al;
reserve f,g for FinSequence of [:CQC-WFF(Al),Proof_Step_Kinds:];

theorem
  p is valid & p => q is valid implies q is valid
proof
A1: TAUT(Al) is being_a_theory by Th11;
  assume p is valid & p => q is valid;
  then  p in TAUT(Al) & p => q in TAUT(Al);
  then  q in TAUT(Al) by A1;
  hence thesis;
end;
