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 Th2:
  p => (q => r) is valid implies (q '&' p) => r is valid
proof
  assume p => (q => r) in TAUT(A);
  then p => (q => r) is valid;
  then (p '&' q) => r is valid by Th1;
  then
A1: (p '&' q) => r in TAUT(A);
  q '&' p => p '&' q in TAUT(A) by CQC_THE1:45;
  hence (q '&' p) => r in TAUT(A) by A1,LUKASI_1:3;
end;
