∴ (x)(Ax→~Bx)↔(y)(Ay→~By)

Logic Theorem; Construct Proof ? (x)(Ax?~Bx)? (y)(Ay?~By)

Answer

1. ∀x∃y (Ax > By) Premise I 2. ∀xAx Assumption I 3. Ac 2 Universal Instantiation I 4. ∃y(Ac > By) 1 Universal Instantiation I 5. Ac > Bd 4 Existential Instantiation I 6. Bd 3, 5 Modus Ponens I 7. ∃yBy 6 Existential Generalization 8. ∀xAx > ∃yBy 2,7 Conditional Proof

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