(4) Consider the proof of the valid formula in the Hilbert's proof system H Step Formula...

 

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(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 {¬B¬A₁¬B→ A₁¬B} =¬B {B¬A,¬BA,¬B}¬B→ A {¬B¬A₁¬B → A₁¬B} - A {¬B→¬A,¬B → A‚¬B} ¦¬B→¬A {¬B¬A,¬B → A‚¬B} = A → B 6. {BA,¬BA,¬B} B {¬B¬A,¬B → A} \¬B→B {¬B¬A,¬B → A} ► (¬B → B) → B {¬BA, BA} + B 5. 7. 8. 9. {¬B¬A} = (¬B→ A) → B +(-¬B¬A) → ((¬B→ A) → B) Provide justification for each step in this proof. You may use any rule or theorem proved or stated in lectures (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 {¬B¬A₁¬B→ A₁¬B} =¬B {B¬A,¬BA,¬B}¬B→ A {¬B¬A₁¬B → A₁¬B} - A {¬B→¬A,¬B → A‚¬B} ¦¬B→¬A {¬B¬A,¬B → A‚¬B} = A → B 6. {BA,¬BA,¬B} B {¬B¬A,¬B → A} \¬B→B {¬B¬A,¬B → A} ► (¬B → B) → B {¬BA, BA} + B 5. 7. 8. 9. {¬B¬A} = (¬B→ A) → B +(-¬B¬A) → ((¬B→ A) → B) Provide justification for each step in this proof. You may use any rule or theorem proved or stated in lectures

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