Theorem mpanr2

An inference based on modus ponens. (Contributed by NM, 3-May-1994.) (Proof shortened by Andrew Salmon, 7-May-2011.) (Proof shortened by Wolf Lammen, 7-Apr-2013.)

Hypotheses
mpanr2.1
\( \vdash \chi \)
mpanr2.2
\( \vdash \varphi \wedge (\psi \wedge \chi) \rightarrow \theta \)
Conclusion
\( \vdash \varphi \wedge \psi \rightarrow \theta \)
Proof
mpanr2.1
l1
jctr _
\( \vdash \psi \rightarrow \psi \wedge \chi \)
mpanr2.2
\( \vdash \varphi \wedge (\psi \wedge \chi) \rightarrow \theta \)
sylan2 l1 _