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Theorem pm5.61 751
 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 biorf 419 . . 3 𝜓 → (𝜑 ↔ (𝜓𝜑)))
2 orcom 401 . . 3 ((𝜓𝜑) ↔ (𝜑𝜓))
31, 2syl6rbb 277 . 2 𝜓 → ((𝜑𝜓) ↔ 𝜑))
43pm5.32ri 673 1 (((𝜑𝜓) ∧ ¬ 𝜓) ↔ (𝜑 ∧ ¬ 𝜓))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   ↔ wb 196   ∨ wo 382   ∧ wa 383 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 197  df-or 384  df-an 385 This theorem is referenced by:  ordtri3  5920  xrnemnf  12164  xrnepnf  12165  hashinfxadd  13386  limcdif  23859  ellimc2  23860  limcmpt  23866  limcres  23869  tglineeltr  25746  tltnle  29992  icorempt2  33528  poimirlem14  33754  xrlttri5d  40012
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