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Theorem aisbnaxb 37946
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 126 . 2  |-  -.  -.  ( ph  <->  ps )
3 df-xor 1401 . 2  |-  ( (
ph  \/_  ps )  <->  -.  ( ph  <->  ps )
)
42, 3mtbir 300 1  |-  -.  ( ph  \/_  ps )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 187    \/_ wxo 1400
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 188  df-xor 1401
This theorem is referenced by:  dandysum2p2e4  38034
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