Theorem bnj170 30764

Description: /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 14-Jun-2011.) (New usage is discouraged.)

Assertion

Ref	Expression
bnj170	|- ( ( ph /\ ps /\ ch ) <-> ( ( ps /\ ch ) /\ ph ) )

Proof of Theorem bnj170

Step	Hyp	Ref	Expression
1		3anrot 1043	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ps /\ ch /\ ph ) )
2		df-3an 1039	. 2 |- ( ( ps /\ ch /\ ph ) <-> ( ( ps /\ ch ) /\ ph ) )
3	1, 2	bitri 264	1 |- ( ( ph /\ ps /\ ch ) <-> ( ( ps /\ ch ) /\ ph ) )

Syntax hints:   <-> wb 196   /\ wa 384   /\ w3a 1037

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

This theorem is referenced by:  bnj543  30963  bnj605  30977  bnj594  30982  bnj607  30986  bnj908  31001  bnj1173  31070