$.$ Suppose that a context$-$free grammar G$=($V$,$T$,$S$,$P$)$ has a production of the form

A$->$xy$,$

where x$,$y$$ in $($V$\backslash$cup T$)^+.$ Prove that if this rule is replaced by

A$->$By$,$

B$->$x$,$

where B$$V$,$ then the resulting grammar is equivalent to the original one.