Hilbert proof systems with hypothesis

Question

This is my set of axioms:

1. $A \rightarrow (B\rightarrow A)$
2. $(A\rightarrow(B\rightarrow C))\rightarrow ((A\rightarrow B) \rightarrow (A \rightarrow C))$
3. $(\neg A \rightarrow B)\rightarrow ((\neg A \rightarrow \neg B)\rightarrow A)$

An I am given:

$$p,\neg p \vdash q$$

Now, from definition, $p$ and $\neg p$ are hypothesis for q to be valid, no? So taking account of that, can I just prove it using only one of the hypothesis?

Answer 1

hypothesis        1 p
hypothesis        2 ¬p
axiom 1           3 (p→(¬q→p))
axiom 1           4 (¬p→(¬q→¬p))
detachment (3, 1) 5 (¬q→p)
detachment (4, 2) 6 (¬q→¬p)
axiom 3           7 ((¬q→p)→((¬q→¬p)→q))
detachment (7, 5) 8 ((¬q→¬p)→q))
detachment (8, 6) 9 q