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Theorem aistbisfiaxb 37955
Description: Given a is equivalent to T., Given b is equivalent to F. there exists a proof for a-xor-b. (Contributed by Jarvin Udandy, 31-Aug-2016.)
Hypotheses
Ref Expression
aistbisfiaxb.1  |-  ( ph  <-> T.  )
aistbisfiaxb.2  |-  ( ps  <-> F.  )
Assertion
Ref Expression
aistbisfiaxb  |-  ( ph  \/_ 
ps )

Proof of Theorem aistbisfiaxb
StepHypRef Expression
1 aistbisfiaxb.1 . . 3  |-  ( ph  <-> T.  )
21aistia 37932 . 2  |-  ph
3 aistbisfiaxb.2 . . 3  |-  ( ps  <-> F.  )
43aisfina 37933 . 2  |-  -.  ps
52, 4abnotbtaxb 37951 1  |-  ( ph  \/_ 
ps )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 187    \/_ wxo 1400   T. wtru 1438   F. wfal 1442
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-an 372  df-xor 1401  df-tru 1440  df-fal 1443
This theorem is referenced by: (None)
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