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Theorem xornbi 1364
Description: A consequence of exclusive or. For decidable propositions this is an equivalence, as seen at xornbidc 1369. (Contributed by Jim Kingdon, 10-Mar-2018.)
Assertion
Ref Expression
xornbi  |-  ( (
ph  \/_  ps )  ->  -.  ( ph  <->  ps )
)

Proof of Theorem xornbi
StepHypRef Expression
1 xorbin 1362 . 2  |-  ( (
ph  \/_  ps )  ->  ( ph  <->  -.  ps )
)
2 pm5.18im 1363 . . 3  |-  ( (
ph 
<->  ps )  ->  -.  ( ph  <->  -.  ps )
)
32con2i 616 . 2  |-  ( (
ph 
<->  -.  ps )  ->  -.  ( ph  <->  ps )
)
41, 3syl 14 1  |-  ( (
ph  \/_  ps )  ->  -.  ( ph  <->  ps )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 104    \/_ wxo 1353
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698
This theorem depends on definitions:  df-bi 116  df-xor 1354
This theorem is referenced by: (None)
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