Self-Distributive Law for Conditional

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Theorem

The following is known as the Self-Distributive Law:


Formulation 1

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


Formulation 2

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


Also see