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Formal proof of distributivity of conjuction

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Proof with natural deduction

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Can anyone clarify the rules for $\forall$ intro and elimination, and $\exists$ intro and elimination?

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Is it possible to prove a contradiction with natural deduction by negating the formula?

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Don't the natural deduction inference rules assume semantics?

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Counterexample for the invalidity of the following

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Proof using natural deduction of $\small\forall x~[A(x)\to\exists y~[B(y)\land C(y,x)]] \vdash\forall x~[\exists y~[A(x)\to(B(y)\land C(y,x))]]$

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179
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Help with natural deduction

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89
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Prove $\vdash \neg(\square F\land p)$ in $KD$

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97
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$\vdash\phi \land \diamond\psi \to \diamond(\psi\land\diamond\phi)$ in KB

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119
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Natural deduction of (p->(p->q))->q on the hypothesis that p

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74
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Categorical proof in natural deduction

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216
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Can axioms be premises in formal proofs?

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123
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Understanding $\lor~E$ in Natural Deduction?

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82
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Gentzen Natural Deduction Quantifier Problem!

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#discrete-mathematics #logic #predicate-logic #quantifiers #natural-deduction

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