Theorem bnj446 30783

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

Assertion

Ref	Expression
bnj446	|- ( ( ph /\ ps /\ ch /\ th ) <-> ( ( ps /\ ch /\ th ) /\ ph ) )

Proof of Theorem bnj446

Step	Hyp	Ref	Expression
1		bnj345 30780	. 2 |- ( ( ps /\ ch /\ th /\ ph ) <-> ( ph /\ ps /\ ch /\ th ) )
2		df-bnj17 30753	. 2 |- ( ( ps /\ ch /\ th /\ ph ) <-> ( ( ps /\ ch /\ th ) /\ ph ) )
3	1, 2	bitr3i 266	1 |- ( ( ph /\ ps /\ ch /\ th ) <-> ( ( ps /\ ch /\ th ) /\ ph ) )

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:  bnj642  30818  bnj667  30822  bnj594  30982