Disjunction of Conditional and Converse

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

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