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Theorem pm5.24 864
Description: Theorem *5.24 of [WhiteheadRussell] p. 124. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm5.24 (¬ ((φ ψ) φ ¬ ψ)) ↔ ((φ ¬ ψ) (ψ ¬ φ)))

Proof of Theorem pm5.24
StepHypRef Expression
1 xor 861 . 2 (¬ (φψ) ↔ ((φ ¬ ψ) (ψ ¬ φ)))
2 dfbi3 863 . 2 ((φψ) ↔ ((φ ψ) φ ¬ ψ)))
31, 2xchnxbi 299 1 (¬ ((φ ψ) φ ¬ ψ)) ↔ ((φ ¬ ψ) (ψ ¬ φ)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 176   wo 357   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-or 359  df-an 360
This theorem is referenced by: (None)
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