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

Theorem aisbnaxb 41399
Description: Given a is equivalent to b, there exists a proof for (not (a xor b)). (Contributed by Jarvin Udandy, 28-Aug-2016.)
Hypothesis
Ref Expression
aisbnaxb.1 (𝜑𝜓)
Assertion
Ref Expression
aisbnaxb ¬ (𝜑𝜓)

Proof of Theorem aisbnaxb
StepHypRef Expression
1 aisbnaxb.1 . . 3 (𝜑𝜓)
21notnoti 137 . 2 ¬ ¬ (𝜑𝜓)
3 df-xor 1505 . 2 ((𝜑𝜓) ↔ ¬ (𝜑𝜓))
42, 3mtbir 312 1 ¬ (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196  wxo 1504
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-xor 1505
This theorem is referenced by:  dandysum2p2e4  41486
  Copyright terms: Public domain W3C validator