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Theorem aisfina 43954
Description: Given a is equivalent to , there exists a proof for not a. (Contributed by Jarvin Udandy, 30-Aug-2016.)
Hypothesis
Ref Expression
aisfina.1 (𝜑 ↔ ⊥)
Assertion
Ref Expression
aisfina ¬ 𝜑

Proof of Theorem aisfina
StepHypRef Expression
1 aisfina.1 . 2 (𝜑 ↔ ⊥)
2 nbfal 1557 . 2 𝜑 ↔ (𝜑 ↔ ⊥))
31, 2mpbir 234 1 ¬ 𝜑
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 209  wfal 1554
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 1545  df-fal 1555
This theorem is referenced by:  aistbisfiaxb  43975  aisfbistiaxb  43976  aifftbifffaibif  43977  aifftbifffaibifff  43978  atnaiana  43979  dandysum2p2e4  44054
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