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Theorem oridm 493
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 pm1.2 492 . 2  |-  ( (
ph  \/  ph )  ->  ph )
2 pm2.07 382 . 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  494  orordi  509  orordir  510  truortru  1272  falorfal  1275  unidm  2937  preqsn  3391  suceloni  4168  tz7.48lem  5902  msq0i  8629  prmdvdsexp  11326  metn0  16004  pdivsq  21041  pm11.7  24483
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