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Theorem pm5.61 1023
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 960 . . 3 𝜓 → (𝜑 ↔ (𝜓𝜑)))
2 orcom 896 . . 3 ((𝜓𝜑) ↔ (𝜑𝜓))
31, 2syl6rbb 279 . 2 𝜓 → ((𝜑𝜓) ↔ 𝜑))
43pm5.32ri 571 1 (((𝜑𝜓) ∧ ¬ 𝜓) ↔ (𝜑 ∧ ¬ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 197  wa 384  wo 873
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 198  df-an 385  df-or 874
This theorem is referenced by:  ordtri3  5946  xrnemnf  12156  xrnepnf  12157  hashinfxadd  13381  limcdif  23945  ellimc2  23946  limcmpt  23952  limcres  23955  tglineeltr  25831  tltnle  30130  icorempt2  33653  poimirlem14  33868  xrlttri5d  40159
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