Theorem biimtrid

A mixed syllogism inference from a nested implication and a biconditional. Useful for substituting an embedded antecedent with a definition. (Contributed by NM, 12-Jan-1993.)

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