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Theorem pm5.16 860
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 pm5.18 345 . . 3 ((φψ) ↔ ¬ (φ ↔ ¬ ψ))
21biimpi 186 . 2 ((φψ) → ¬ (φ ↔ ¬ ψ))
3 imnan 411 . 2 (((φψ) → ¬ (φ ↔ ¬ ψ)) ↔ ¬ ((φψ) (φ ↔ ¬ ψ)))
42, 3mpbi 199 1 ¬ ((φψ) (φ ↔ ¬ ψ))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 176   wa 358
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 177  df-an 360
This theorem is referenced by: (None)
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