Theorem bnj255 30771

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

Assertion

Ref	Expression
bnj255	|- ( ( ph /\ ps /\ ch /\ th ) <-> ( ph /\ ps /\ ( ch /\ th ) ) )

Proof of Theorem bnj255

Step	Hyp	Ref	Expression
1		bnj251 30768	. 2 |- ( ( ph /\ ps /\ ch /\ th ) <-> ( ph /\ ( ps /\ ( ch /\ th ) ) ) )
2		3anass 1042	. 2 |- ( ( ph /\ ps /\ ( ch /\ th ) ) <-> ( ph /\ ( ps /\ ( ch /\ th ) ) ) )
3	1, 2	bitr4i 267	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:  bnj964  31013  bnj998  31026  bnj1033  31037  bnj1175  31072