The

reversal

of the antecedent and the consequent of the conditional

\begin{equation*} P \implies Q \end{equation*}

in the form

\begin{align*} & P \impliedby Q \\ \qor & Q \implies P, \end{align*}

which, unlike the contrapositive, is

not equivalent to the original statement,

so

\begin{equation*} (Q \implies P) \> \not \equiv \> (P \implies Q), \end{equation*}

but is

equivalent to its inverse,

so

\begin{equation*} (Q \implies P) \> \equiv \> (\lnot P \implies \lnot Q). \end{equation*}

(Levin 2021, sec. 0.2)

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• Example
• Proof