Theorem mpanl2

An inference based on modus ponens. (Contributed by NM, 16-Aug-1994.) (Proof shortened by Andrew Salmon, 7-May-2011.)

Hypotheses
mpanl2.1
\( \vdash \psi \)
mpanl2.2
\( \vdash \varphi \wedge \psi \wedge \chi \rightarrow \theta \)
Conclusion
\( \vdash \varphi \wedge \chi \rightarrow \theta \)
Proof
mpanl2.1
l1
jctr _
\( \vdash \varphi \rightarrow \varphi \wedge \psi \)
mpanl2.2
\( \vdash \varphi \wedge \psi \wedge \chi \rightarrow \theta \)
sylan l1 _