Theorem mpd3an23

An inference based on modus ponens. (Contributed by NM, 4-Dec-2006.)

Hypotheses
mpd3an23.1
\( \vdash \varphi \rightarrow \psi \)
mpd3an23.2
\( \vdash \varphi \rightarrow \chi \)
mpd3an23.3
\( \vdash \varphi \wedge \psi \wedge \chi \rightarrow \theta \)
Conclusion
\( \vdash \varphi \rightarrow \theta \)
Proof
l0
id
\( \vdash \varphi \rightarrow \varphi \)
l1
mpd3an23.1
\( \vdash \varphi \rightarrow \psi \)
l2
mpd3an23.2
\( \vdash \varphi \rightarrow \chi \)
mpd3an23.3
\( \vdash \varphi \wedge \psi \wedge \chi \rightarrow \theta \)
syl3anc l0 l1 l2 _