Theorem 3anan12 947

Description: Convert triple conjunction to conjunction, then commute. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)

Assertion

Ref	Expression
3anan12	|- ((ph /\ ps /\ ch) <-> (ps /\ (ph /\ ch)))

Proof of Theorem 3anan12

Step	Hyp	Ref	Expression
1		3ancoma 941	. 2 |- ((ph /\ ps /\ ch) <-> (ps /\ ph /\ ch))
2		3anass 938	. 2 |- ((ps /\ ph /\ ch) <-> (ps /\ (ph /\ ch)))
3	1, 2	bitri 240	1 |- ((ph /\ ps /\ ch) <-> (ps /\ (ph /\ ch)))

Syntax hints:   <-> wb 176   /\ wa 358   /\ w3a 934

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936

This theorem is referenced by:  2reu5lem3  3044