Category:Conditional is Left Distributive over Conjunction

This category contains pages concerning Conditional is Left Distributive over Conjunction:

The implication operator is left distributive over the conjunction operator:

Formulation 1

$p \implies \paren {q \land r} \dashv \vdash \paren {p \implies q} \land \paren {p \implies r}$

Formulation 2

$\vdash \paren {p \implies \paren {q \land r} } \iff \paren {\paren {p \implies q} \land \paren {p \implies r} }$