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Theorem pm5.61 994
Description: Theorem *5.61 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 30-Jun-2013.)
Assertion
Ref Expression
pm5.61 (((𝜑𝜓) ∧ ¬ 𝜓) ↔ (𝜑 ∧ ¬ 𝜓))

Proof of Theorem pm5.61
StepHypRef Expression
1 orel2 884 . . 3 𝜓 → ((𝜑𝜓) → 𝜑))
2 orc 861 . . 3 (𝜑 → (𝜑𝜓))
31, 2impbid1 226 . 2 𝜓 → ((𝜑𝜓) ↔ 𝜑))
43pm5.32ri 576 1 (((𝜑𝜓) ∧ ¬ 𝜓) ↔ (𝜑 ∧ ¬ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 207  wa 396  wo 841
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842
This theorem is referenced by:  ordtri3  6220  xrnemnf  12500  xrnepnf  12501  hashinfxadd  13734  limcdif  24401  ellimc2  24402  limcmpt  24408  limcres  24411  tglineeltr  26344  tltnle  30576  icorempo  34514  poimirlem14  34787  xrlttri5d  41425
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