Theorem bnj422 30781

Description: /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 14-Jun-2011.) (New usage is discouraged.)

Assertion

Ref	Expression
bnj422	|- ( ( ph /\ ps /\ ch /\ th ) <-> ( ch /\ th /\ ph /\ ps ) )

Proof of Theorem bnj422

Step	Hyp	Ref	Expression
1		bnj345 30780	. 2 |- ( ( ph /\ ps /\ ch /\ th ) <-> ( th /\ ph /\ ps /\ ch ) )
2		bnj345 30780	. 2 |- ( ( th /\ ph /\ ps /\ ch ) <-> ( ch /\ th /\ ph /\ ps ) )
3	1, 2	bitri 264	1 |- ( ( ph /\ ps /\ ch /\ th ) <-> ( ch /\ th /\ ph /\ ps ) )

Syntax hints:   <-> wb 196   /\ w-bnj17 30752

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  df-3an 1039  df-bnj17 30753

This theorem is referenced by:  bnj432  30782  bnj535  30960  bnj558  30972