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Theorem aisfina 41488
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 1608 . 2 𝜑 ↔ (𝜑 ↔ ⊥))
31, 2mpbir 221 1 ¬ 𝜑
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196  wfal 1601
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  df-tru 1599  df-fal 1602
This theorem is referenced by:  aistbisfiaxb  41509  aisfbistiaxb  41510  aifftbifffaibif  41511  aifftbifffaibifff  41512  atnaiana  41513  dandysum2p2e4  41588
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