Disjunction of Conditional and Converse

Theorem
Given any two statements, one of them implies the other.
 * $\vdash \left({p \implies q}\right) \lor \left({q \implies p}\right)$

That is, given any conditional, either it is true or its converse is.

Also see

 * Smullyan's Drinking Principle


 * Paradoxes of Material Implication, in which category this result is sometimes grouped