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