Theorem anidm 396

Description: Idempotent law for conjunction. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 14-Mar-2014.)

Assertion

Ref	Expression
anidm	|- ( ( ph /\ ph ) <-> ph )

Proof of Theorem anidm

Step	Hyp	Ref	Expression
1		pm4.24 395	. 2 |- ( ph <-> ( ph /\ ph ) )
2	1	bicomi 132	1 |- ( ( ph /\ ph ) <-> ph )

Syntax hints:   /\ wa 104   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  anidmdbi  398  anandi  590  anandir  591  truantru  1421  falanfal  1424  truxortru  1439  truxorfal  1440  falxortru  1441  falxorfal  1442  sbnf2  2009  2eu4  2147  inidm  3382  ralidm  3561  opcom  4296  opeqsn  4298  poirr  4355  rnxpid  5118  xp11m  5122  fununi  5343  brprcneu  5571  erinxp  6698  dom2lem  6865  dmaddpi  7440  dmmulpi  7441  enq0ref  7548  enq0tr  7549  expap0  10716  sqap0  10753  xrmaxiflemcom  11593  gcddvds  12317  isnsg2  13572  eqger  13593  xmeter  14941