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;
