Prove the following sequents using the propositional logic rules plus UE, UI, and EI.
¬∃x(Fx∧Gx) ⊢ ∀x(Fx→¬Gx)
¬∃x(Fx→P) ⊢ ∀xFx
∀xFx→P ⊢ ∃x(Fx→P)
Prove the following sequents using the propositional logic rules plus UE, UI, EI, and EE.
∃x(Fx→Gx) ⊢ ∀xFx→∃xGx
∀x∃y(Fy→Gx) ⊢ ∀yFy→∀xGx
∃x(Fx∨Gx),¬∃xFx ⊢ ∃yGy
P→∃xFx ⊢ ∃x(P→Fx)