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First Order Logic


I am currently working through a textbook on First Order Logic and am currently at the stage of doing complex proofs. The proof system being used in this textbook is a natural deduction system. I am really struggling on two questions that I thought maybe someone in this forum could help me with. The idea of these questions is to demonstrated the following claims. The single turnstile used here is supposed to denote the existence of proofs, that the sentences prior to it can prove the one after it. If someone could help me with these two questions I would be eternally grateful as I am really struggling. Thank you.

1. ∃xFx, ∃yGy, ¬∃x∃y¬x = y ⊢ ∃z(Fz ∧ Gz)

2. ∀x∀y∀z((Rxy ∧ Rxz) → y = z), ¬∃x∀y(¬Rxy ∨ ¬Fy) ⊢ ∀x∀y(Rxy → Fy)

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