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Theorem pm4.53 512
Description: Theorem *4.53 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm4.53 (¬ (𝜑 ∧ ¬ 𝜓) ↔ (¬ 𝜑𝜓))

Proof of Theorem pm4.53
StepHypRef Expression
1 pm4.52 511 . . 3 ((𝜑 ∧ ¬ 𝜓) ↔ ¬ (¬ 𝜑𝜓))
21con2bii 346 . 2 ((¬ 𝜑𝜓) ↔ ¬ (𝜑 ∧ ¬ 𝜓))
32bicomi 214 1 (¬ (𝜑 ∧ ¬ 𝜓) ↔ (¬ 𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196  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 197  df-or 384  df-an 385
This theorem is referenced by:  undif3  3921  undif3OLD  3922  itg2addnclem  33591  cdleme32e  36050  undif3VD  39432
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