Proof for the immortality of the human soul

The following proof has been derived using St. Thomas Aquinas' Summa Theologiae, I, 75.

Every intellect is that which can know all corporeal things.
Every human soul is an intellect.
Therefore, every human soul is that which can know all corporeal things.

Nothing that can know all corporeal things is corporeal.
Every human soul is that which can know all corporeal things.
Therefore, no human soul is corporeal.
Which is to say that every human soul is non-corporeal.

Every non-corporeal thing is that which has an operation that body does not share.
Every human soul is non-corporeal.
Therefore, every human soul is that which has an operation body does not share.

Everything that has an operation body does not share is that which has an operation in itself.
Every human soul is that which has an operation body does not share.
Therefore, every human soul is that which has an operation in itself.

Everything that has an operation in itself is that which subsists in itself.
Every human soul is that which has an operation in itself.
Therefore, every human soul is that which subsists in itself.

Everything that subsists in itself is a substance.
Every human soul is that which subsists in itself.
Therefore, every human soul is a substance.

No substance is corruptible per accidens.
Every human soul is a substance.
Therefore, no human soul is corruptible per accidens.

Every form is an act.
Every human soul is a form.
Therefore, every human soul is an act.

Every act is that which exists by virtue of itself.
Every human soul is an act.
Therefore, every human soul is that which exists by virtue of itself.

Nothing that exists by virtue of itself is corruptible per se.
Every human soul is that which exists by virtue of itself.
Therefore, no human soul is corruptible per se.

If the human soul is corruptible, then the human soul is corruptible per se or the human soul is corruptible per accidens.
No human soul is corruptible per se and no human soul is corruptible per accidens.
Therefore, no human soul is corruptible.
Which is to say that the human soul is incorruptible

That which is incorruptible is immortal.
The human soul is incorruptible.
Therefore, the human soul is immortal.