Theorem 3expa

Exportation from triple to double conjunction. (Contributed by NM, 20-Aug-1995.) (Revised to shorten 3exp and pm3.2an3 by Wolf Lammen, 22-Jun-2022.)

Hypothesis
3exp.1
\( \vdash \varphi \wedge \psi \wedge \chi \rightarrow \theta \)
Conclusion
\( \vdash \varphi \wedge \psi \wedge \chi \rightarrow \theta \)
Proof
l0
df-3an
\( \vdash \varphi \wedge \psi \wedge \chi \leftrightarrow \varphi \wedge \psi \wedge \chi \)
3exp.1
\( \vdash \varphi \wedge \psi \wedge \chi \rightarrow \theta \)
sylbir l0 _