Theorem bnj257 30773

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

Assertion

Ref	Expression
bnj257	|- ( ( ph /\ ps /\ ch /\ th ) <-> ( ph /\ ps /\ th /\ ch ) )

Proof of Theorem bnj257

Step	Hyp	Ref	Expression
1		ancom 466	. . 3 |- ( ( ch /\ th ) <-> ( th /\ ch ) )
2	1	anbi2i 730	. 2 |- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ph /\ ps ) /\ ( th /\ ch ) ) )
3		bnj256 30772	. 2 |- ( ( ph /\ ps /\ ch /\ th ) <-> ( ( ph /\ ps ) /\ ( ch /\ th ) ) )
4		bnj256 30772	. 2 |- ( ( ph /\ ps /\ th /\ ch ) <-> ( ( ph /\ ps ) /\ ( th /\ ch ) ) )
5	2, 3, 4	3bitr4i 292	1 |- ( ( ph /\ ps /\ ch /\ th ) <-> ( ph /\ ps /\ th /\ ch ) )

Syntax hints:   <-> wb 196   /\ wa 384   /\ 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:  bnj258  30774  bnj334  30779  bnj543  30963  bnj929  31006