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Theorem pm5.61 716
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 671 . . 3 𝜓 → (𝜑 ↔ (𝜓𝜑)))
2 orcom 655 . . 3 ((𝜓𝜑) ↔ (𝜑𝜓))
31, 2syl6rbb 190 . 2 𝜓 → ((𝜑𝜓) ↔ 𝜑))
43pm5.32ri 436 1 (((𝜑𝜓) ∧ ¬ 𝜓) ↔ (𝜑 ∧ ¬ 𝜓))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wa 101  wb 102  wo 637
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in2 553  ax-io 638
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  pm5.75  878  excxor  1283  xrnemnf  8770  xrnepnf  8771
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