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Theorem oridm 494
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 pm1.2 493 . 2  |-  ( (
ph  \/  ph )  ->  ph )
2 pm2.07 383 . 2  |-  ( ph  ->  ( ph  \/  ph ) )
31, 2impbii 178 1  |-  ( (
ph  \/  ph )  <->  ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 174    \/ wo 355
This theorem is referenced by:  pm4.25  495  orordi  510  orordir  511  truortru  1275  falorfal  1278  unidm  2941  preqsn  3399  suceloni  4177  tz7.48lem  5914  msq0i  8818  msq0d  8820  prmdvdsexp  11914  metn0  16628  pdivsq  21991  pm11.7  25431
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 175  df-or 357
Copyright terms: Public domain