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Theorem xornbi 1322
Description: A consequence of exclusive or. For decidable propositions this is an equivalence, as seen at xornbidc 1327. (Contributed by Jim Kingdon, 10-Mar-2018.)
Assertion
Ref Expression
xornbi  |-  ( (
ph  \/_  ps )  ->  -.  ( ph  <->  ps )
)

Proof of Theorem xornbi
StepHypRef Expression
1 xorbin 1320 . 2  |-  ( (
ph  \/_  ps )  ->  ( ph  <->  -.  ps )
)
2 pm5.18im 1321 . . 3  |-  ( (
ph 
<->  ps )  ->  -.  ( ph  <->  -.  ps )
)
32con2i 592 . 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 103    \/_ wxo 1311
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-io 665
This theorem depends on definitions:  df-bi 115  df-xor 1312
This theorem is referenced by: (None)
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