Goal: (φ→¬K¬φ) System: S5(m) using derived rules: true 1. S5(m) ⊢ (K¬φ→¬φ) (A3) 2. S5(m) ⊢ (¬¬φ→¬K¬φ) (CP:1) 3. S5(m) ⊢ (φ↔¬¬φ) (A1) 4. S5(m) ⊢ (φ→¬K¬φ) (SUB:3,2)