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Theorem pm4.52 512
Description: Theorem *4.52 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 5-Nov-2012.)
Assertion
Ref Expression
pm4.52 ((𝜑 ∧ ¬ 𝜓) ↔ ¬ (¬ 𝜑𝜓))

Proof of Theorem pm4.52
StepHypRef Expression
1 annim 441 . 2 ((𝜑 ∧ ¬ 𝜓) ↔ ¬ (𝜑𝜓))
2 imor 428 . 2 ((𝜑𝜓) ↔ (¬ 𝜑𝜓))
31, 2xchbinx 324 1 ((𝜑 ∧ ¬ 𝜓) ↔ ¬ (¬ 𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 196  wo 383  wa 384
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 385  df-an 386
This theorem is referenced by:  pm4.53  513  ordtri3  5757  ifpim123g  37671
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