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 2 added 773 characters in body edited Nov 24 '18 at 8:16 Graham Kemp 1,28822 silver badges1111 bronze badges The form of 'v elimination' is a Proof by Cases. You raise two subproofs, by assuming the cases of a given disjunction in turn, with the goal in each to derive the same conclusion. ``````| A v B Given [Premise, Assumption, or Derived] | - | |_ A Assumption | | : | | C Derived | - | |_ B Assumption | | : | | C Derived | - | C v Elimination `````` So you will have ``````|_ [f] S(f) Assumption | (D(f) ^ L(f)) v (C(f) ^ S(f)) Universal Elimination | |_ D(f) ^ L(f) Assumption | | L(f) Conjunction Elimination | | : | | ~~F(f) Negation Elimination | | F(f) Double Negation Elimination | - | |_ C(f) ^ S(f) Assumption | | C(f) Conjunction Elimination | | C(f) -> F(f) Universal Elimination | | F(f) Disjunction Elimination | F(f) Disjunction Elimination Ax (S(x) -> F(x)) Universal Introduction `````` The form of 'v elimination' is a Proof by Cases. You raise two subproofs, by assuming the cases of a given disjunction in turn, with the goal in each to derive the same conclusion. ``````| A v B Given [Premise, Assumption, or Derived] | - | |_ A Assumption | | : | | C Derived | - | |_ B Assumption | | : | | C Derived | - | C v Elimination `````` The form of 'v elimination' is a Proof by Cases. You raise two subproofs, by assuming the cases of a given disjunction in turn, with the goal in each to derive the same conclusion. ``````| A v B Given [Premise, Assumption, or Derived] | - | |_ A Assumption | | : | | C Derived | - | |_ B Assumption | | : | | C Derived | - | C v Elimination `````` So you will have ``````|_ [f] S(f) Assumption | (D(f) ^ L(f)) v (C(f) ^ S(f)) Universal Elimination | |_ D(f) ^ L(f) Assumption | | L(f) Conjunction Elimination | | : | | ~~F(f) Negation Elimination | | F(f) Double Negation Elimination | - | |_ C(f) ^ S(f) Assumption | | C(f) Conjunction Elimination | | C(f) -> F(f) Universal Elimination | | F(f) Disjunction Elimination | F(f) Disjunction Elimination Ax (S(x) -> F(x)) Universal Introduction `````` 1 answered Nov 24 '18 at 7:41 Graham Kemp 1,28822 silver badges1111 bronze badges The form of 'v elimination' is a Proof by Cases. You raise two subproofs, by assuming the cases of a given disjunction in turn, with the goal in each to derive the same conclusion. ``````| A v B Given [Premise, Assumption, or Derived] | - | |_ A Assumption | | : | | C Derived | - | |_ B Assumption | | : | | C Derived | - | C v Elimination ``````