Implication is Left Distributive over Conjunction/Forward Implication/Formulation 2/Proof

Theorem

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

Proof
Let us use substitution instances as follows:


 * align="right" | 2 ||
 * align="right" | 2
 * $\psi$
 * Sequent Introduction
 * 1
 * Implication is Left Distributive over Conjunction: Formulation 1
 * Implication is Left Distributive over Conjunction: Formulation 1

Using substitution instances leads us back to:
 * $\left({p \implies \left({q \land r}\right)}\right) \implies \left({\left({p \implies q}\right) \land \left({p \implies r}\right)}\right)$