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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  2940  preqsn  3394  suceloni  4171  tz7.48lem  5908  msq0i  8809  msq0d  8811  prmdvdsexp  11898  metn0  16611  pdivsq  21974  pm11.7  25414
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