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Theorem oridm 674
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
StepHypRef Expression
1 pm1.2 673 . 2  |-  ( (
ph  \/  ph )  ->  ph )
2 pm2.07 656 . 2  |-  ( ph  ->  ( ph  \/  ph ) )
31, 2impbii 117 1  |-  ( (
ph  \/  ph )  <->  ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 98    \/ wo 629
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  pm4.25  675  orordi  690  orordir  691  truortru  1296  falorfal  1299  truxortru  1310  falxorfal  1313  unidm  3083  preqsn  3543  reapirr  7544  reapti  7546  lt2msq  7828  nn0ge2m1nn  8214  absext  9539
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