Rules of Classical Predicate Calculus
In the following rules, is exactly like except for having the term everywhere has the free variable .
- Universal Introduction (or Universal Generalization)
Restriction 1: does not occur in .
Restriction 2: is not mentioned in any hypothesis or undischarged assumptions.
- Universal Elimination (or Universal Instantiation)
Restriction: No free occurrence of in falls within the scope of a quantifier quantifying a variable occurring in .
- Existential Introduction (or Existential Generalization)
Restriction: No free occurrence of in falls within the scope of a quantifier quantifying a variable occurring in .
- Existential Elimination (or Existential Instantiation)
Restriction 1: No free occurrence of in falls within the scope of a quantifier quantifying a variable occurring in .
Restriction 2: There is no occurrence, free or bound, of in .
Read more about this topic: List Of Rules Of Inference
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