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Theorem pm5.16 952
Description: Theorem *5.16 of [WhiteheadRussell] p. 124. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 17-Oct-2013.)
Assertion
Ref Expression
pm5.16 ¬ ((𝜑𝜓) ∧ (𝜑 ↔ ¬ 𝜓))

Proof of Theorem pm5.16
StepHypRef Expression
1 pm5.18 370 . . 3 ((𝜑𝜓) ↔ ¬ (𝜑 ↔ ¬ 𝜓))
21biimpi 206 . 2 ((𝜑𝜓) → ¬ (𝜑 ↔ ¬ 𝜓))
3 imnan 437 . 2 (((𝜑𝜓) → ¬ (𝜑 ↔ ¬ 𝜓)) ↔ ¬ ((𝜑𝜓) ∧ (𝜑 ↔ ¬ 𝜓)))
42, 3mpbi 220 1 ¬ ((𝜑𝜓) ∧ (𝜑 ↔ ¬ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 196  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-an 385
This theorem is referenced by: (None)
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