Theorem bnj250 30767

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

Assertion

Ref	Expression
bnj250	|- ( ( ph /\ ps /\ ch /\ th ) <-> ( ph /\ ( ( ps /\ ch ) /\ th ) ) )

Proof of Theorem bnj250

Step	Hyp	Ref	Expression
1		df-bnj17 30753	. 2 |- ( ( ph /\ ps /\ ch /\ th ) <-> ( ( ph /\ ps /\ ch ) /\ th ) )
2		3anass 1042	. . 3 |- ( ( ph /\ ps /\ ch ) <-> ( ph /\ ( ps /\ ch ) ) )
3	2	anbi1i 731	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th ) <-> ( ( ph /\ ( ps /\ ch ) ) /\ th ) )
4		anass 681	. 2 |- ( ( ( ph /\ ( ps /\ ch ) ) /\ th ) <-> ( ph /\ ( ( ps /\ ch ) /\ th ) ) )
5	1, 3, 4	3bitri 286	1 |- ( ( ph /\ ps /\ ch /\ th ) <-> ( ph /\ ( ( ps /\ ch ) /\ th ) ) )

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:  bnj251  30768  bnj252  30769  bnj345  30780