Theorem biimtrrid

A mixed syllogism inference from a nested implication and a biconditional. (Contributed by NM, 21-Jun-1993.)

Hypotheses
biimtrrid.1
\( \vdash \psi \leftrightarrow \varphi \)
biimtrrid.2
\( \vdash \chi \rightarrow \psi \rightarrow \theta \)
Conclusion
\( \vdash \chi \rightarrow \varphi \rightarrow \theta \)
Proof
biimtrrid.1
l1
biimpri _
\( \vdash \varphi \rightarrow \psi \)
biimtrrid.2
\( \vdash \chi \rightarrow \psi \rightarrow \theta \)
syl5 l1 _