Theorem nic-swap

The connector -/\ is symmetric. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)

Conclusion
\( \vdash (\theta \barwedge \varphi) \barwedge ((\varphi \barwedge \theta) \barwedge (\varphi \barwedge \theta)) \)
Proof
l0
nic-id
\( \vdash \varphi \barwedge (\varphi \barwedge \varphi) \)
nic-ax
\( \vdash (\varphi \barwedge (\varphi \barwedge \varphi)) \barwedge ((\varphi \barwedge (\varphi \barwedge \varphi)) \barwedge ((\theta \barwedge \varphi) \barwedge ((\varphi \barwedge \theta) \barwedge (\varphi \barwedge \theta)))) \)
nic-mp l0 _