Principle of Commutation

Theorem

Formulation 1

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

Formulation 2

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