Theorem oridm 707

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		pm1.2 706	. 2 |- ( ( ph \/ ph ) -> ph )
2		pm2.07 689	. 2 |- ( ph -> ( ph \/ ph ) )
3	1, 2	impbii 124	1 |- ( ( ph \/ ph ) <-> ph )

Syntax hints:   <-> wb 103   \/ wo 662

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 663

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  pm4.25  708  orordi  723  orordir  724  truortru  1337  falorfal  1340  truxortru  1351  falxorfal  1354  unidm  3116  preqsn  3575  reapirr  7744  reapti  7746  lt2msq  8031  nn0ge2m1nn  8415  absext  10087  prmdvdsexp  10671  sqpweven  10697  2sqpwodd  10698