When definite descriptions are given Russell’s analysis, their properties follow from the properties of the logical constants used in their analysis, but the description operator requires special treatment.
8.6.1. The role of definite descriptions in entailment
The basic principle for definite descriptions is a law describing the interpretation of the description operator discussed in 8.4.2.
8.6.2. Derivations for the description operator
Because definite descriptions are not formulas but have formulas as components, the derivation rule for them takes a different form from those we have seen so far.