Theorem mtoi

Modus tollens inference. (Contributed by NM, 5-Jul-1994.) (Proof shortened by Wolf Lammen, 15-Sep-2012.)

Hypotheses
mtoi.1
\( \vdash \neg \chi \)
mtoi.2
\( \vdash \varphi \rightarrow \psi \rightarrow \chi \)
Conclusion
\( \vdash \varphi \rightarrow \neg \psi \)
Proof
mtoi.1
l1
a1i _
\( \vdash \varphi \rightarrow \neg \chi \)
mtoi.2
\( \vdash \varphi \rightarrow \psi \rightarrow \chi \)
mtod l1 _