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Theorem pm5.61 996
 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 886 . . 3 𝜓 → ((𝜑𝜓) → 𝜑))
2 orc 863 . . 3 (𝜑 → (𝜑𝜓))
31, 2impbid1 227 . 2 𝜓 → ((𝜑𝜓) ↔ 𝜑))
43pm5.32ri 578 1 (((𝜑𝜓) ∧ ¬ 𝜓) ↔ (𝜑 ∧ ¬ 𝜓))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   ↔ wb 208   ∧ wa 398   ∨ wo 843 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 209  df-an 399  df-or 844 This theorem is referenced by:  ordtri3  6220  xrnemnf  12504  xrnepnf  12505  hashinfxadd  13738  limcdif  24466  ellimc2  24467  limcmpt  24473  limcres  24476  tglineeltr  26409  tltnle  30642  icorempo  34619  poimirlem14  34893  xrlttri5d  41533
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