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Theorem pm4.54 512
Description: Theorem *4.54 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 5-Nov-2012.)
Assertion
Ref Expression
pm4.54 ((¬ 𝜑𝜓) ↔ ¬ (𝜑 ∨ ¬ 𝜓))

Proof of Theorem pm4.54
StepHypRef Expression
1 df-an 384 . 2 ((¬ 𝜑𝜓) ↔ ¬ (¬ 𝜑 → ¬ 𝜓))
2 pm4.66 434 . 2 ((¬ 𝜑 → ¬ 𝜓) ↔ (𝜑 ∨ ¬ 𝜓))
31, 2xchbinx 322 1 ((¬ 𝜑𝜓) ↔ ¬ (𝜑 ∨ ¬ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  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:  pm4.55  513
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