Theorem stoic4b

Stoic logic Thema 4 version b. This is version b, which is with the phrase "or both". See stoic4a for more information. (Contributed by David A. Wheeler, 17-Feb-2019.)

Hypotheses
stoic4b.1
\( \vdash \varphi \wedge \psi \rightarrow \chi \)
stoic4b.2
\( \vdash (\chi \wedge \varphi \wedge \psi) \wedge \theta \rightarrow \tau \)
Conclusion
\( \vdash \varphi \wedge \psi \wedge \theta \rightarrow \tau \)
Proof
stoic4b.1
l1
3adant3 _
\( \vdash \varphi \wedge \psi \wedge \theta \rightarrow \chi \)
l2
simp1
\( \vdash \varphi \wedge \psi \wedge \theta \rightarrow \varphi \)
l3
simp2
\( \vdash \varphi \wedge \psi \wedge \theta \rightarrow \psi \)
l4
simp3
\( \vdash \varphi \wedge \psi \wedge \theta \rightarrow \theta \)
stoic4b.2
\( \vdash (\chi \wedge \varphi \wedge \psi) \wedge \theta \rightarrow \tau \)
syl31anc l1 l2 l3 l4 _