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

$Axy,$

where $x,$yin$(WT{)}^{+}.$ Prove that if this rule is replaced by

$ABy,$

$Bx,$

where $B!$inV, then the resulting grammar is equivalent to the original one. $[10$ pts$]$