Theorem 3anan12 980

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 975	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ps /\ ph /\ ch ) )
2		3anass 972	. 2 |- ( ( ps /\ ph /\ ch ) <-> ( ps /\ ( ph /\ ch ) ) )
3	1, 2	bitri 183	1 |- ( ( ph /\ ps /\ ch ) <-> ( ps /\ ( ph /\ ch ) ) )

Syntax hints:   /\ wa 103   <-> wb 104   /\ w3a 968

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 970

This theorem is referenced by:  fncnv  5254  dff1o2  5437