Rule of Material Implication/Formulation 1/Forward Implication

Theorem

 * $p \implies q \vdash \neg p \lor q$

Proof

 * align="right" | 2 ||
 * align="right" |
 * $p \lor \neg p$
 * LEM
 * (None)
 * (None)


 * align="right" | 6 ||
 * align="right" | 1, 5
 * $q$
 * $\implies \mathcal E$
 * 1, 5
 * 1, 5


 * align="right" | 8 ||
 * align="right" | 1
 * $\neg p \lor q$
 * $\lor \mathcal E$
 * 2, 3-4, 5-7
 * 2, 3-4, 5-7