Suppose the following have been established or assumed:

Question

Axiom 1: p ->~y

Axiom 2: ~q ->r

Theorem 1: p -> ~z

Theorem 2: x -> either q or z

Theorem 3: r -> either x or y

Write a two-column proof of the proposition p -> q

Answer 1

This is as far as I can get:

Assume p.
It follow from (Axiom 1) that ~y.
It follows from (Thrm. 1) that ~z.

Are you sure you copied down the Axioms and Theorems correctly?

If we also assumed ~x, then
it follows from (Thrm. 3) that ~r.
Finally it follows from (Axiom 2) that q.

Therefor, (p and ~x) -> q
Q.E.D.?