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Theorem abnotataxb 30099
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 455 . . . 4  |-  ( ps 
/\  -.  ph )
43olci 391 . . 3  |-  ( (
ph  /\  -.  ps )  \/  ( ps  /\  -.  ph ) )
5 xor 886 . . 3  |-  ( -.  ( ph  <->  ps )  <->  ( ( ph  /\  -.  ps )  \/  ( ps  /\  -.  ph )
) )
64, 5mpbir 209 . 2  |-  -.  ( ph 
<->  ps )
7 df-xor 1352 . 2  |-  ( (
ph  \/_  ps )  <->  -.  ( ph  <->  ps )
)
86, 7mpbir 209 1  |-  ( ph  \/_ 
ps )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184    \/ wo 368    /\ wa 369    \/_ wxo 1351
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 185  df-or 370  df-an 371  df-xor 1352
This theorem is referenced by:  aisfbistiaxb  30103
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