Theorem 2falsed

Two falsehoods are equivalent (deduction form). (Contributed by NM, 11-Oct-2013.) (Proof shortened by Wolf Lammen, 11-Apr-2024.)

Hypotheses
2falsed.1
\( \vdash \varphi \rightarrow \neg \psi \)
2falsed.2
\( \vdash \varphi \rightarrow \neg \chi \)
Conclusion
\( \vdash \varphi \rightarrow (\psi \leftrightarrow \chi) \)
Proof
l0
2falsed.1
2falsed.2
2thd l0 _
con4bid _