List questions from natural-deduction

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Prove $\vdash \neg \neg A \leftrightarrow A$ in intuitionistic logic

Published on 25 Mar 2026 - 17:37

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Modal logic - Show that if $\vdash \Diamond T$ holds, $\vdash \Box A \to \Diamond A$ holds

Published on 25 Mar 2026 - 19:10

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Formal proof with first order logic axioms.

Published on 06 Dec 2016 - 0:14

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Proving 'Law of Excluded Middle' in Fitch system

Published on 11 Dec 2016 - 19:09

260

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$⊢ ∀x∀y(f(x) \neq f(y) → x \neq y)$

Published on 13 Dec 2016 - 11:45

96

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$∃x¬(\varphi ∨ \psi) → ∃x(¬\varphi ∨ ¬\psi)$ and $∃y(\varphi ∧ \psi) → (∀x$ $\varphi ∧ ∀y$ $\psi)$

Published on 13 Dec 2016 - 12:07

941

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Peano axioms: $∀y∀x(x×y = y×x)$, using induction in $y$

Published on 13 Dec 2016 - 12:27

1.8k

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There exists x such that P(x) and there exists x such that not P(x) implies that there exists x,y such that x does not equal to y?

Published on 21 Dec 2016 - 22:02

3k

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Main differences and relations between Sequent Calculus and Natural Deduction

Published on 23 Feb 2026 - 10:15

143

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First Order Logic Inference Rule

Published on 28 Dec 2016 - 12:36

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Quantifier inference rules restrictions

Published on 30 Dec 2016 - 14:50

1k

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Natural deduction technique/question

Published on 02 Jan 2017 - 20:55

156

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$⊢(\phi ∨ \psi) → (¬\phi → \psi)$

Published on 02 Jan 2017 - 23:31

192

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Peano/Presburger axioms - "find" numbers lower or equal than another number

Published on 24 Mar 2026 - 23:46

List Question

Natural deduction: how to prove the argument below

Prove $\vdash \neg \neg A \leftrightarrow A$ in intuitionistic logic

Modal logic - Show that if $\vdash \Diamond T$ holds, $\vdash \Box A \to \Diamond A$ holds

Formal proof with first order logic axioms.

Proving 'Law of Excluded Middle' in Fitch system

$⊢ ∀x∀y(f(x) \neq f(y) → x \neq y)$

$∃x¬(\varphi ∨ \psi) → ∃x(¬\varphi ∨ ¬\psi)$ and $∃y(\varphi ∧ \psi) → (∀x$ $\varphi ∧ ∀y$ $\psi)$

Peano axioms: $∀y∀x(x×y = y×x)$, using induction in $y$

There exists x such that P(x) and there exists x such that not P(x) implies that there exists x,y such that x does not equal to y?

Main differences and relations between Sequent Calculus and Natural Deduction

First Order Logic Inference Rule

Quantifier inference rules restrictions

Natural deduction technique/question

$⊢(\phi ∨ \psi) → (¬\phi → \psi)$

Peano/Presburger axioms - "find" numbers lower or equal than another number

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