Summary: Some equivalences for manipulation of first-order formulas.
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The following equivalences are in addition to
those of propositional logic.
In these,
| Equivalence | ∀ Variant | ∃ Variant |
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| Complementation of Quantifiers |
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| Interchanging Quantifiers |
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| Distribution of Quantifiers |
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Distribution of Quantifiers |
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| Renaming |
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Simplification of Quantifiers |
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Simplification of Quantifiers |
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When citing Distribution of Quantifiers,
say what you're distributing over what: e.g.,
“
distribute ∀ over ∨ (with
In
renaming,
the notation
This set of equivalences isn't actually quite complete.
For instance,