Theorem mpanl1

An inference based on modus ponens. (Contributed by NM, 16-Aug-1994.) (Proof shortened by Wolf Lammen, 7-Apr-2013.)

Hypotheses
mpanl1.1
\( \vdash \varphi \)
mpanl1.2
\( \vdash \varphi \wedge \psi \wedge \chi \rightarrow \theta \)
Conclusion
\( \vdash \psi \wedge \chi \rightarrow \theta \)
Proof
mpanl1.1
l1
jctl _
\( \vdash \psi \rightarrow \varphi \wedge \psi \)
mpanl1.2
\( \vdash \varphi \wedge \psi \wedge \chi \rightarrow \theta \)
sylan l1 _