Theorem an43 867

Description: Rearrangement of 4 conjuncts. (Contributed by Rodolfo Medina, 24-Sep-2010.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)

Assertion

Ref	Expression
an43	|- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ph /\ th ) /\ ( ps /\ ch ) ) )

Proof of Theorem an43

Step	Hyp	Ref	Expression
1		an42 866	. 2 |- ( ( ( ph /\ th ) /\ ( ps /\ ch ) ) <-> ( ( ph /\ ps ) /\ ( ch /\ th ) ) )
2	1	bicomi 214	1 |- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ph /\ th ) /\ ( ps /\ ch ) ) )

Syntax hints:   <-> wb 196   /\ wa 384

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 197  df-an 386

This theorem is referenced by:  an3  868  prtlem15  34160