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Theorem pm5.61 745
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 276 . 2 𝜓 → ((𝜑𝜓) ↔ 𝜑))
43pm5.32ri 668 1 (((𝜑𝜓) ∧ ¬ 𝜓) ↔ (𝜑 ∧ ¬ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 195  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 196  df-or 384  df-an 385
This theorem is referenced by:  pm5.75OLD  975  ordtri3  5676  xrnemnf  11827  xrnepnf  11828  hashinfxadd  13035  limcdif  23446  ellimc2  23447  limcmpt  23453  limcres  23456  tglineeltr  25326  tltnle  28993  icorempt2  32375  poimirlem14  32593  xrlttri5d  38436
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