Theorem 3jcad

Deduction conjoining the consequents of three implications. (Contributed by NM, 25-Sep-2005.)

Hypotheses
3jcad.1
\( \vdash \varphi \rightarrow \psi \rightarrow \chi \)
3jcad.2
\( \vdash \varphi \rightarrow \psi \rightarrow \theta \)
3jcad.3
\( \vdash \varphi \rightarrow \psi \rightarrow \tau \)
Conclusion
\( \vdash \varphi \rightarrow \psi \rightarrow \chi \wedge \theta \wedge \tau \)
Proof
3jcad.1
l1
imp _
3jcad.2
l3
imp _
3jcad.3
imp _
3jca l1 l3 _
ex _