Theorem 3anan32 989

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 980	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ps ) /\ ch ) )
2		an32 562	. 2 |- ( ( ( ph /\ ps ) /\ ch ) <-> ( ( ph /\ ch ) /\ ps ) )
3	1, 2	bitri 184	1 |- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ch ) /\ ps ) )

Syntax hints:   /\ wa 104   <-> wb 105   /\ w3a 978

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 980

This theorem is referenced by:  anandi3r  992  dff1o3  5459