Theorem mt3i

Modus tollens inference. (Contributed by NM, 26-Mar-1995.) (Proof shortened by Wolf Lammen, 15-Sep-2012.)

Hypotheses
mt3i.1
\( \vdash \neg \chi \)
mt3i.2
\( \vdash \varphi \rightarrow \neg \psi \rightarrow \chi \)
Conclusion
\( \vdash \varphi \rightarrow \psi \)
Proof
mt3i.1
l1
a1i _
\( \vdash \varphi \rightarrow \neg \chi \)
mt3i.2
\( \vdash \varphi \rightarrow \neg \psi \rightarrow \chi \)
mt3d l1 _