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 Th26:
  X1 |-| X2 & X1 \/ Y |- Z implies X2 \/ Y |- Z
proof
  assume that
A1: X1 |-| X2 and
A2: X1 \/ Y |- Z;
  X1 \/ Y |-| X2 \/ Y by A1,Th25;
  then Cn(X1 \/ Y) = Cn(X2 \/ Y) by Th20;
  then Z c= Cn(X2 \/ Y) by A2,Th7;
  hence thesis by Th7;
end;
