Confusion of Bound Variables

Mistake
Let $$\mathbf A$$ be the WFF of Predicate Calculus:
 * $$\forall x: \exists y: x < y$$

Suppose we wished to substitute $$y$$ for $$x$$.

If we paid no heed to whether $$y$$ were free for $x$, we would obtain:
 * $$\forall y: \exists y: y < y$$.

This is plainly false for the natural numbers, but $$\forall x: \exists y: x < y$$ is true (just take $$y = x + 1$$).

This problem is called confusion of bound variables.