Theorem 3anan32 946

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

Assertion

Ref	Expression
3anan32	|- ((ph /\ ps /\ ch) <-> ((ph /\ ch) /\ ps))

Proof of Theorem 3anan32

Step	Hyp	Ref	Expression
1		df-3an 936	. 2 |- ((ph /\ ps /\ ch) <-> ((ph /\ ps) /\ ch))
2		an32 773	. 2 |- (((ph /\ ps) /\ ch) <-> ((ph /\ ch) /\ ps))
3	1, 2	bitri 240	1 |- ((ph /\ ps /\ ch) <-> ((ph /\ ch) /\ ps))

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: (None)