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Theorem pm4.55 916
Description: Theorem *4.55 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm4.55 (¬ (¬ 𝜑𝜓) ↔ (𝜑 ∨ ¬ 𝜓))

Proof of Theorem pm4.55
StepHypRef Expression
1 pm4.54 915 . . 3 ((¬ 𝜑𝜓) ↔ ¬ (𝜑 ∨ ¬ 𝜓))
21con2bii 346 . 2 ((𝜑 ∨ ¬ 𝜓) ↔ ¬ (¬ 𝜑𝜓))
32bicomi 214 1 (¬ (¬ 𝜑𝜓) ↔ (𝜑 ∨ ¬ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196  wa 382  wo 826
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 197  df-an 383  df-or 827
This theorem is referenced by:  chrelat2i  29558  hlrelat2  35204  ifpnot23  38342
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