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Theorem pm5.61 744
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 418 . . 3 𝜓 → (𝜑 ↔ (𝜓𝜑)))
2 orcom 400 . . 3 ((𝜓𝜑) ↔ (𝜑𝜓))
31, 2syl6rbb 275 . 2 𝜓 → ((𝜑𝜓) ↔ 𝜑))
43pm5.32ri 667 1 (((𝜑𝜓) ∧ ¬ 𝜓) ↔ (𝜑 ∧ ¬ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 194  wo 381  wa 382
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 195  df-or 383  df-an 384
This theorem is referenced by:  pm5.75OLD  974  ordtri3  5658  xrnemnf  11784  xrnepnf  11785  hashinfxadd  12983  limcdif  23359  ellimc2  23360  limcmpt  23366  limcres  23369  tglineeltr  25240  tltnle  28795  icorempt2  32174  poimirlem14  32392  xrlttri5d  38235
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