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  1401  falanfal  1404  truxortru  1419  truxorfal  1420  falxortru  1421  falxorfal  1422  sbnf2  1981  2eu4  2119  inidm  3346  ralidm  3525  opcom  4252  opeqsn  4254  poirr  4309  rnxpid  5065  xp11m  5069  fununi  5286  brprcneu  5510  erinxp  6611  dom2lem  6774  dmaddpi  7326  dmmulpi  7327  enq0ref  7434  enq0tr  7435  expap0  10552  sqap0  10589  xrmaxiflemcom  11259  gcddvds  11966  isnsg2  13068  eqger  13088  xmeter  13975