reserve A for QC-alphabet;
reserve X,T for Subset of CQC-WFF(A);
reserve F,G,H,p,q,r,t for Element of CQC-WFF(A);
reserve s,h for QC-formula of A;
reserve x,y for bound_QC-variable of A;
reserve f for FinSequence of [:CQC-WFF(A),Proof_Step_Kinds:];
reserve i,j for Element of NAT;

theorem Th4:
  (p '&' q) => r is valid implies q => (p => r) is valid
proof
A1: q '&' p => p '&' q in TAUT(A) by CQC_THE1:45;
  assume (p '&' q) => r in TAUT(A);
  then q '&' p => r in TAUT(A) by A1,LUKASI_1:3;
  then q '&' p => r is valid;
  then q => (p => r) is valid by Th3;
  hence q => (p => r) in TAUT(A);
end;
