Implication is Left Distributive over Conjunction/Reverse Implication/Formulation 1/Proof

Theorem

 * $\left({p \implies q}\right) \land \left({p \implies r}\right) \vdash p \implies \left({q \land r}\right)$

Proof

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 * align="right" | 1
 * $\left({p \land p}\right) \implies \left({q \land r}\right)$
 * Sequent Introduction
 * 1
 * Praeclarum Theorema
 * Praeclarum Theorema


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 * align="right" | 3
 * $p \land p$
 * Sequent Introduction
 * 3
 * Rule of Idempotence
 * Rule of Idempotence