Theorem sylanbr

A syllogism inference. (Contributed by NM, 18-May-1994.)

Hypotheses
sylanbr.1
\( \vdash \psi \leftrightarrow \varphi \)
sylanbr.2
\( \vdash \psi \wedge \chi \rightarrow \theta \)
Conclusion
\( \vdash \varphi \wedge \chi \rightarrow \theta \)
Proof
sylanbr.1
l1
biimpri _
\( \vdash \varphi \rightarrow \psi \)
sylanbr.2
\( \vdash \psi \wedge \chi \rightarrow \theta \)
sylan l1 _