reserve A for QC-alphabet;
reserve p, q, r, s, p1, q1 for Element of CQC-WFF(A),
  X, Y, Z, X1, X2 for Subset of CQC-WFF(A),
  h for QC-formula of A,
  x, y for bound_QC-variable of A,
  n for Element of NAT;

theorem Th41:
  p is closed & p |- q implies p => q is valid
proof
  assume that
A1: p is closed and
A2: p |- q;
  {}(CQC-WFF(A)) \/ {p} |- q by A2;
  then {}(CQC-WFF(A)) |- p => q by A1,CQC_THE2:92;
  hence thesis by CQC_THE1:def 9;
end;
