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.