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Theorem oridm 673
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 ((φ φ) ↔ φ)

Proof of Theorem oridm
StepHypRef Expression
1 pm1.2 672 . 2 ((φ φ) → φ)
2 pm2.07 655 . 2 (φ → (φ φ))
31, 2impbii 117 1 ((φ φ) ↔ φ)
Colors of variables: wff set class
Syntax hints:  wb 98   wo 628
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 629
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  pm4.25  674  orordi  689  orordir  690  truortru  1293  falorfal  1296  truxortru  1307  falxorfal  1310  unidm  3080  preqsn  3537  reapirr  7341  reapti  7343  lt2msq  7613  nn0ge2m1nn  7998
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