διὸ ψθχή ἐστιν ἐντελέχεια ἠ πρώτη σώματος φυσικοῦ δυνάμει ζωὴν ἔχοντος
Αριστοτελους, ΠΕΡΙ ΨΥΧΗΣ, Β 1, 412a28-29
The soul is the first actuality of a natural body with the potentiality of having life
Aristotle, de Anima II. 1, 412a28-29
Demonstration of the definition of the soul from Aristotle, de Anima II, 2 according to Thomas Aquinas, In de Anima II, lt. 2-4.
Major: The principle of life is the first actuality and substantial form of the living thing
Minor: The soul is the principle of life
Conclusion: The soul is the first actuality and substantial form of the living thing
The middle is the definition of the principle of life.
Defense of the major: The living composite material substance is composed of two substantial principles, the matter and the form. The matter is in potentiality and the form is in actuality, and so takes priority over the material principle (you know this from the Physics I. 7-9; II. 1; Metaphysics Θ 8; Λ 6-7). The matter cannot be the principle of life’s first actuality, because matter is a principle of potentiality, whereas form is a principle of actuality (cf. Metaphysics Z 3, 17; Θ 6-9). Hence, the form as the first actuality is the principle of life.
Defense of the minor: As is clear from induction not all bodies are living, and so it is due to a principle other than corporeality that some bodies are living. This principle is called soul, i.e., animation, which is the principle of nutrition, sensation, movement, and intellection. The soul is the primary principle of these, for even they all (except for the intellect) clearly exist through the body, i.e., it is in and through the body that we have health and sensation, we are primarily said to have health and sensation on account of the soul. We do not live on account of the body, but because of the soul. Hence, the soul is called the principle of life, nutrition, sensation, and so on.