Theorem oridm 709

Description: Idempotent law for disjunction. Theorem *4.25 of [WhiteheadRussell] p. 117. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 16-Apr-2011.) (Proof shortened by Wolf Lammen, 10-Mar-2013.)

Assertion

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

Proof of Theorem oridm

Step	Hyp	Ref	Expression
1		pm1.2 708	. 2 |- ( ( ph \/ ph ) -> ph )
2		pm2.07 691	. 2 |- ( ph -> ( ph \/ ph ) )
3	1, 2	impbii 124	1 |- ( ( ph \/ ph ) <-> ph )

Syntax hints:   <-> wb 103   \/ wo 664

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  pm4.25  710  orordi  725  orordir  726  truortru  1341  falorfal  1344  truxortru  1355  falxorfal  1358  unidm  3143  preqsn  3619  reapirr  8054  reapti  8056  lt2msq  8347  nn0ge2m1nn  8733  absext  10496  prmdvdsexp  11405  sqpweven  11431  2sqpwodd  11432