Writing a Hilbert-style Proof for $(A ∧ (¬B)) ⊢ (¬(A → B)$

167 Views Asked by At

I've been trying to write a Hilbert-style proof using the Axioms and Rules of Inference for propositional logic, but I keep getting stuck at step 3.

$$(A ∧(¬B)) ⊢ (¬(A → B)$$

  1. $(A ∧ (¬B))$ (Hypothesis)
  2. $A = ¬B = (A ∨ ¬B)$ (Golden Rule, eqn)
  3. $A = (A → ¬B)$ (Implication, Leib, c-part A=P, p-fresh)