Law of Identity

Theorem
Every proposition entails itself:

Formulation 2
A seemingly trivial rule, but can be surprisingly useful to get a particular formula into the right place in a proof.

Interpretation by Models
Clearly, every model of $P$ is a model of $P$.

Thus by definition of semantic consequence:
 * $P \models P$

Also known as
This is also known as the rule of repetition.

Also see

 * Biconditional is Reflexive, where $\vdash p \iff p$ is shown.