Theorem mt2bi

A false consequent falsifies an antecedent. (Contributed by NM, 19-Aug-1993.) (Proof shortened by Wolf Lammen, 12-Nov-2012.)

Hypothesis
mt2bi.1
\( \vdash \varphi \)
Conclusion
\( \vdash \neg \psi \leftrightarrow \psi \rightarrow \neg \varphi \)
Proof
mt2bi.1
l1
a1bi _
\( \vdash \neg \psi \leftrightarrow \varphi \rightarrow \neg \psi \)
con2b
\( \vdash \varphi \rightarrow \neg \psi \leftrightarrow \psi \rightarrow \neg \varphi \)
bitri l1 _