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Theorem pm4.54 479
Description: Theorem *4.54 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 5-Nov-2012.)
Assertion
Ref Expression
pm4.54 ((¬ φ ψ) ↔ ¬ (φ ¬ ψ))

Proof of Theorem pm4.54
StepHypRef Expression
1 df-an 360 . 2 ((¬ φ ψ) ↔ ¬ (¬ φ → ¬ ψ))
2 pm4.66 409 . 2 ((¬ φ → ¬ ψ) ↔ (φ ¬ ψ))
31, 2xchbinx 301 1 ((¬ φ ψ) ↔ ¬ (φ ¬ ψ))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  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:  pm4.55  480
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