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Logic Theorem; Construct Proof

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∴ (x)(Ax→~Bx)↔(y)(Ay→~By)

Jan 4th, 2015


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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Jan 6th, 2015

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