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Theorem aistbisfiaxb 27991
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 27968 . 2  |-  ph
3 aistbisfiaxb.2 . . 3  |-  ( ps  <->  F.  )
43aisfina 27969 . 2  |-  -.  ps
52, 4abnotbtaxb 27987 1  |-  ( ph  \/_ 
ps )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    \/_ wxo 1295    T. wtru 1307    F. wfal 1308
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 177  df-an 360  df-xor 1296  df-tru 1310  df-fal 1311
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