Theorem mpan2

An inference based on modus ponens. (Contributed by NM, 16-Sep-1993.) (Proof shortened by Wolf Lammen, 19-Nov-2012.)

Hypotheses
mpan2.1
\( \vdash \psi \)
mpan2.2
\( \vdash \varphi \wedge \psi \rightarrow \chi \)
Conclusion
\( \vdash \varphi \rightarrow \chi \)
Proof
mpan2.1
l1
a1i _
\( \vdash \varphi \rightarrow \psi \)
mpan2.2
\( \vdash \varphi \wedge \psi \rightarrow \chi \)
mpdan l1 _