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 Th1:
  p => (q => r) is valid implies (p '&' q) => r is valid
proof
A1: (p => (q => r)) => ((p '&' q) => r) in TAUT(A) by PROCAL_1:32;
  assume p => (q => r) in TAUT(A);
  hence (p '&' q) => r in TAUT(A) by A1,CQC_THE1:46;
end;
