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Theorem pm5.61 1003
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 891 . . 3 𝜓 → ((𝜑𝜓) → 𝜑))
2 orc 868 . . 3 (𝜑 → (𝜑𝜓))
31, 2impbid1 225 . 2 𝜓 → ((𝜑𝜓) ↔ 𝜑))
43pm5.32ri 575 1 (((𝜑𝜓) ∧ ¬ 𝜓) ↔ (𝜑 ∧ ¬ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 206  wa 395  wo 848
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 207  df-an 396  df-or 849
This theorem is referenced by:  ordtri3  6420  xrnemnf  13159  xrnepnf  13160  hashinfxadd  14424  tltnle  18467  limcdif  25911  ellimc2  25912  limcmpt  25918  limcres  25921  tglineeltr  28639  icorempo  37352  poimirlem14  37641  xrlttri5d  45295
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