theorem Th17:
  <*x*> ==>. y implies <*z/"y*> ==>. z/"x & <*y\z*> ==>. x\z
proof
  assume
A1: <*x*> ==>. y;
A2: <*z*> ==>. z by Def18;
  then
A3: <*z/"y*>^<*x*> ==>. z by A1,Lm4;
  <*x*>^<*y\z*> ==>. z by A1,A2,Lm7;
  hence thesis by A3,Def18;
end;
