Proposotional logic derivation

Question

Show that (φ ∧ ψ) ↔ ¬(φ → ¬ψ) is derivable.

I have derived ¬(φ → ¬ψ) from (φ ∧ ψ) by assuming (φ → ¬ψ) and (φ ∧ ψ) and deducing a contradiction. By cancellation of the hypotheses I can then conclude that (φ ∧ ψ) → ¬(φ → ¬ψ) is derivable, but I can't seem to figure out how to do the implication the other way around.

Answer 1

Hint: Assume $\lnot$φ. Then derive a contradiction. Infer φ. Then assume $\lnot$$\psi$ and derive a contradiction. Infer $\psi$.