Labeled Formula

A formula AA can be labeled when it exists as a pair AαA^{\alpha} if α\alpha is either a true or false value.

We can also have a set of formulas, then we can use:

Φα:={Aα∣A∈Φ}\boldsymbol{\Phi}^\alpha:=\left\{A^\alpha \mid A \in \boldsymbol{\Phi}\right\}