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- Vx(P(x)) <=> Vy(P(y))
- 3x(P(x)) <=> 3y(P(y))

Bound Variable allows the user to substitute any bound variable for another bound variable, given that the second bound variable does not appear anywhere in the scope of the quantifier of the first bound variable. For example, if it is known that Vx(Vy(P(x) ^ P(y))), an invalid use of bound variable would be to state that Vx(Vx(P(x) ^ P(x))).

As an equivalence rule, bound variable uses only one reference, and can work on any part of the sentence.