Theorem bnj253 30770

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

Assertion

Ref	Expression
bnj253	|- ( ( ph /\ ps /\ ch /\ th ) <-> ( ( ph /\ ps ) /\ ch /\ th ) )

Proof of Theorem bnj253

Step	Hyp	Ref	Expression
1		bnj248 30766	. 2 |- ( ( ph /\ ps /\ ch /\ th ) <-> ( ( ( ph /\ ps ) /\ ch ) /\ th ) )
2		df-3an 1039	. 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:  bnj543  30963  bnj558  30972  bnj594  30982  bnj917  31004  bnj929  31006  bnj944  31008  bnj978  31019  bnj998  31026  bnj1006  31029