D.D. Warrior Lady's effect

SoilentG

CoG iTrader
D.D. Warrior Lady:

When this card battles with your opponent's monster, after damage calculation you can remove from play the opponent's monster and this card.

If D.D Warrior Lady attacks a monster and destroys it, you can choose to activate her effect. The question I have is whether she can opt to remove the monster destroyed but not herself. The way I read it, it's one effect with an AND so if the player chooses to remove the destroyed monster from play then she goes too.

Is that right?
 
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