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Theorem ainaiaandna 43958
Description: Given a, a implies it is not the case a implies a self contradiction. (Contributed by Jarvin Udandy, 7-Sep-2020.)
Hypothesis
Ref Expression
ainaiaandna.1 𝜑
Assertion
Ref Expression
ainaiaandna (𝜑 → ¬ (𝜑 → (𝜑 ∧ ¬ 𝜑)))

Proof of Theorem ainaiaandna
StepHypRef Expression
1 ainaiaandna.1 . . 3 𝜑
21atnaiana 43957 . 2 ¬ (𝜑 → (𝜑 ∧ ¬ 𝜑))
32a1i 11 1 (𝜑 → ¬ (𝜑 → (𝜑 ∧ ¬ 𝜑)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wa 399
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-an 400  df-tru 1545  df-fal 1555
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator