Inside Collection (Course): Intro to Logic
Summary: Some equivalences for manipulation of firstorder formulas.
The following equivalences are in addition to
those of propositional logic.
In these,
Equivalence  ∀ Variant  ∃ Variant 

Complementation of Quantifiers 


Interchanging Quantifiers 


Distribution of Quantifiers 









Distribution of Quantifiers 






Renaming 


Simplification of Quantifiers 


Simplification of Quantifiers 


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,