Theorem bnj345 30780

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
bnj345	|- ( ( ph /\ ps /\ ch /\ th ) <-> ( th /\ ph /\ ps /\ ch ) )

Proof of Theorem bnj345

Step	Hyp	Ref	Expression
1		bnj334 30779	. 2 |- ( ( ph /\ ps /\ ch /\ th ) <-> ( ch /\ ph /\ ps /\ th ) )
2		bnj250 30767	. . 3 |- ( ( ch /\ ph /\ ps /\ th ) <-> ( ch /\ ( ( ph /\ ps ) /\ th ) ) )
3		3anass 1042	. . 3 |- ( ( ch /\ ( ph /\ ps ) /\ th ) <-> ( ch /\ ( ( ph /\ ps ) /\ th ) ) )
4	2, 3	bitr4i 267	. 2 |- ( ( ch /\ ph /\ ps /\ th ) <-> ( ch /\ ( ph /\ ps ) /\ th ) )
5		3anrev 1049	. . 3 |- ( ( ch /\ ( ph /\ ps ) /\ th ) <-> ( th /\ ( ph /\ ps ) /\ ch ) )
6		bnj250 30767	. . . 4 |- ( ( th /\ ph /\ ps /\ ch ) <-> ( th /\ ( ( ph /\ ps ) /\ ch ) ) )
7		3anass 1042	. . . 4 |- ( ( th /\ ( ph /\ ps ) /\ ch ) <-> ( th /\ ( ( ph /\ ps ) /\ ch ) ) )
8	6, 7	bitr4i 267	. . 3 |- ( ( th /\ ph /\ ps /\ ch ) <-> ( th /\ ( ph /\ ps ) /\ ch ) )
9	5, 8	bitr4i 267	. 2 |- ( ( ch /\ ( ph /\ ps ) /\ th ) <-> ( th /\ ph /\ ps /\ ch ) )
10	1, 4, 9	3bitri 286	1 |- ( ( ph /\ ps /\ ch /\ th ) <-> ( th /\ ph /\ ps /\ ch ) )

Syntax hints:   <-> wb 196   /\ wa 384   /\ w3a 1037   /\ 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:  bnj422  30781  bnj446  30783  bnj929  31006  bnj964  31013