(4) Consider the proof of the valid formula in the Hilbert's proof system H Step Formula 1. 2. 3. 4. (BA) ((B A) B) 10. 11. Justification {BAB AB} =B {BA,BA,B}B A {BAB AB} - A {BA,B AB} BA {BA,B AB} = A B 6. {BA,BA,B} B {BA,B A} \BB {BA,B A} (B B) B {BA, BA} + B 5. 7. 8. 9. {BA} = (B A) B +(-BA) ((B A) B) Provide justification for each step in this proof. You may use any rule or theorem proved or stated in lectures