Theorem bnj290 30776

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

Assertion

Ref	Expression
bnj290	|- ( ( ph /\ ps /\ ch /\ th ) <-> ( ph /\ ch /\ th /\ ps ) )

Proof of Theorem bnj290

Step	Hyp	Ref	Expression
1		3anrot 1043	. . 3 |- ( ( ps /\ ch /\ th ) <-> ( ch /\ th /\ ps ) )
2	1	anbi2i 730	. 2 |- ( ( ph /\ ( ps /\ ch /\ th ) ) <-> ( ph /\ ( ch /\ th /\ ps ) ) )
3		bnj252 30769	. 2 |- ( ( ph /\ ps /\ ch /\ th ) <-> ( ph /\ ( ps /\ ch /\ th ) ) )
4		bnj252 30769	. 2 |- ( ( ph /\ ch /\ th /\ ps ) <-> ( ph /\ ( ch /\ th /\ ps ) ) )
5	2, 3, 4	3bitr4i 292	1 |- ( ( ph /\ ps /\ ch /\ th ) <-> ( ph /\ ch /\ th /\ ps ) )

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:  bnj291  30777  bnj334  30779