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Theorem notbinot1 34008
Description: Simplification rule of negation across a biimplication. (Contributed by Giovanni Mascellani, 15-Sep-2017.)
Assertion
Ref Expression
notbinot1 (¬ (¬ 𝜑𝜓) ↔ (𝜑𝜓))

Proof of Theorem notbinot1
StepHypRef Expression
1 nbbn 372 . . 3 ((¬ 𝜑𝜓) ↔ ¬ (𝜑𝜓))
21bicomi 214 . 2 (¬ (𝜑𝜓) ↔ (¬ 𝜑𝜓))
32con1bii 345 1 (¬ (¬ 𝜑𝜓) ↔ (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196
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 197
This theorem is referenced by:  bicontr  34009
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