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Theorem abnotataxb 27899
Description: Assuming not a, b, there exists a proof a-xor-b.) (Contributed by Jarvin Udandy, 31-Aug-2016.)
Hypotheses
Ref Expression
abnotataxb.1  |-  -.  ph
abnotataxb.2  |-  ps
Assertion
Ref Expression
abnotataxb  |-  ( ph  \/_ 
ps )

Proof of Theorem abnotataxb
StepHypRef Expression
1 abnotataxb.2 . . . . 5  |-  ps
2 abnotataxb.1 . . . . 5  |-  -.  ph
31, 2pm3.2i 443 . . . 4  |-  ( ps 
/\  -.  ph )
43olci 382 . . 3  |-  ( (
ph  /\  -.  ps )  \/  ( ps  /\  -.  ph ) )
5 xor 863 . . 3  |-  ( -.  ( ph  <->  ps )  <->  ( ( ph  /\  -.  ps )  \/  ( ps  /\  -.  ph )
) )
64, 5mpbir 202 . 2  |-  -.  ( ph 
<->  ps )
7 df-xor 1315 . 2  |-  ( (
ph  \/_  ps )  <->  -.  ( ph  <->  ps )
)
86, 7mpbir 202 1  |-  ( ph  \/_ 
ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 178    \/ wo 359    /\ wa 360    \/_ wxo 1314
This theorem is referenced by:  aisfbistiaxb  27903
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 179  df-or 361  df-an 362  df-xor 1315
  Copyright terms: Public domain W3C validator