Database: Proper substatement

Definition 21: A statement \psi is said to be a proper substatement (or to be properly a component of) a statement \phi if we have one of the following:
(a) \phi is a conjunction (\xi \wedge \chi) and \psi is a substatement of \xi or of \chi .
(b) \phi is a negation \neg \xi and \psi is a substatement of \xi .
(c) \phi is an existence statement \exists x \xi (with x being some variable) and \psi is a substatement of \xi .

This database entry builds on the following:

  1. Terminology: Class, statement
  2. Definition: Conjunction
  3. Definition: Negation
  4. Definition: Existential quantification
  5. Definition: Substatement