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Theorem bicontr 35518
Description: Biimplication of its own negation is a contradiction. (Contributed by Giovanni Mascellani, 15-Sep-2017.)
Assertion
Ref Expression
bicontr ((¬ 𝜑𝜑) ↔ ⊥)

Proof of Theorem bicontr
StepHypRef Expression
1 biid 264 . . 3 (𝜑𝜑)
2 notbinot1 35517 . . 3 (¬ (¬ 𝜑𝜑) ↔ (𝜑𝜑))
31, 2mpbir 234 . 2 ¬ (¬ 𝜑𝜑)
43bifal 1554 1 ((¬ 𝜑𝜑) ↔ ⊥)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 209  wfal 1550
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  df-tru 1541  df-fal 1551
This theorem is referenced by: (None)
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