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Why is this assumption needed in the Universational Introduction?

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Analysis I (Terence Tao)—Free and bound variables

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A question on a specific kind of prenex normal form

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What would be the translation of the following sentence in logic?

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Translation of predicate logic into english confusion

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How do I prove this in natural deduction calculus?

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Predicate logic - structure where two things exist and aren't the same?

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If $\alpha\to\beta$ is a tautology, then $\beta$ or $\lnot\alpha$ are tautologies.

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Defining an FOL language

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what is the meaning of this FOL sentence?

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143
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Nested Quantifier Negation and Scoping

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169
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How to connect statements in predicate logic?

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154
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definition of image in axiomatic set theory

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286
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FOL equivalence, operations and usage of quantifiers

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71
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Determining if a given formula is a first order formula

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