Theorem mpan2i

An inference based on modus ponens. (Contributed by NM, 10-Apr-1994.) (Proof shortened by Wolf Lammen, 19-Nov-2012.)

Hypotheses
mpan2i.1
\( \vdash \chi \)
mpan2i.2
\( \vdash \varphi \rightarrow \psi \wedge \chi \rightarrow \theta \)
Conclusion
\( \vdash \varphi \rightarrow \psi \rightarrow \theta \)
Proof
mpan2i.1
l1
a1i _
\( \vdash \varphi \rightarrow \chi \)
mpan2i.2
\( \vdash \varphi \rightarrow \psi \wedge \chi \rightarrow \theta \)
mpan2d l1 _