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Theorem aisbnaxb 27857
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  |-  ( ph  <->  ps )
Assertion
Ref Expression
aisbnaxb  |-  -.  ( ph  \/_  ps )

Proof of Theorem aisbnaxb
StepHypRef Expression
1 aisbnaxb.1 . . 3  |-  ( ph  <->  ps )
21notnoti 118 . 2  |-  -.  -.  ( ph  <->  ps )
3 df-xor 1315 . 2  |-  ( (
ph  \/_  ps )  <->  -.  ( ph  <->  ps )
)
42, 3mtbir 292 1  |-  -.  ( ph  \/_  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 178    \/_ wxo 1314
This theorem is referenced by:  dandysum2p2e4  27921
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 179  df-xor 1315
  Copyright terms: Public domain W3C validator