Theorem bnj251 30768

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

Assertion

Ref	Expression
bnj251	|- ( ( ph /\ ps /\ ch /\ th ) <-> ( ph /\ ( ps /\ ( ch /\ th ) ) ) )

Proof of Theorem bnj251

Step	Hyp	Ref	Expression
1		bnj250 30767	. 2 |- ( ( ph /\ ps /\ ch /\ th ) <-> ( ph /\ ( ( ps /\ ch ) /\ th ) ) )
2		anass 681	. . 3 |- ( ( ( ps /\ ch ) /\ th ) <-> ( ps /\ ( ch /\ th ) ) )
3	2	anbi2i 730	. 2 |- ( ( ph /\ ( ( ps /\ ch ) /\ th ) ) <-> ( ph /\ ( ps /\ ( ch /\ th ) ) ) )
4	1, 3	bitri 264	1 |- ( ( ph /\ ps /\ ch /\ th ) <-> ( ph /\ ( ps /\ ( ch /\ th ) ) ) )

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:  bnj255  30771  bnj535  30960  bnj570  30975  bnj953  31009  bnj1110  31050