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Theorem pm5.61 1000
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 890 . . 3 𝜓 → ((𝜑𝜓) → 𝜑))
2 orc 866 . . 3 (𝜑 → (𝜑𝜓))
31, 2impbid1 224 . 2 𝜓 → ((𝜑𝜓) ↔ 𝜑))
43pm5.32ri 577 1 (((𝜑𝜓) ∧ ¬ 𝜓) ↔ (𝜑 ∧ ¬ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 205  wa 397  wo 846
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 206  df-an 398  df-or 847
This theorem is referenced by:  ordtri3  6401  xrnemnf  13097  xrnepnf  13098  hashinfxadd  14345  tltnle  18375  limcdif  25393  ellimc2  25394  limcmpt  25400  limcres  25403  tglineeltr  27882  icorempo  36232  poimirlem14  36502  xrlttri5d  43993
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