Users' Mathboxes Mathbox for Jarvin Udandy < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  aisfina Structured version   Visualization version   GIF version

Theorem aisfina 41585
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 1643 . 2 𝜑 ↔ (𝜑 ↔ ⊥))
31, 2mpbir 221 1 ¬ 𝜑
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196  wfal 1636
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 1634  df-fal 1637
This theorem is referenced by:  aistbisfiaxb  41606  aisfbistiaxb  41607  aifftbifffaibif  41608  aifftbifffaibifff  41609  atnaiana  41610  dandysum2p2e4  41685
  Copyright terms: Public domain W3C validator