Principle of Dilemma/Formulation 1

Theorem
If both a premise and its negation imply the conclusion, then the conclusion must be true independently of any premises.
 * $\left({p \implies q}\right) \land \left({\neg p \implies q}\right) \dashv \vdash q$

This can be expressed as two separate theorems:

Also see

 * Proof by Cases