Frobenius Theorem, a Proof

Question

I would find the proof of Frobenius Theorem (Differential Topology).

Statement: Let $\mathbb{S}$ an overdetermined homogenuous first order PDEs system. $\mathbb{S}$ admits unique maximal solution if and only if $\mathbb{S}$ is involutive.

I know that following conditions are equivalent:

1. $\mathbb{S}$ is integrable,
2. $\mathbb{S}$ is completely integrable,
3. $\mathbb{S}$ is involutive.

Where could I find the proof I required? Thank you so much

Answer 1

You can find a proof in chapter 1 of Warner's book Foundations of differentiable manifolds and Lie groups, starting on page 41.