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Theorem pm4.81 397
Description: A formula is equivalent to its negation implying it. Theorem *4.81 of [WhiteheadRussell] p. 122. Note that the second step, using pm2.24 124, could also use ax-1 6. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm4.81 ((¬ 𝜑𝜑) ↔ 𝜑)

Proof of Theorem pm4.81
StepHypRef Expression
1 pm2.18 128 . 2 ((¬ 𝜑𝜑) → 𝜑)
2 pm2.24 124 . 2 (𝜑 → (¬ 𝜑𝜑))
31, 2impbii 212 1 ((¬ 𝜑𝜑) ↔ 𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 209
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 210
This theorem is referenced by:  ifpimimb  40210  ifpimim  40215
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