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Theorem axorbtnotaiffb 27871
Description: Given a is exclusive to b, there exists a proof for (not (a if-and-only-if b)) df-xor is a closed form of this. (Contributed by Jarvin Udandy, 7-Sep-2016.)
Hypothesis
Ref Expression
axorbtnotaiffb.1  |-  ( ph \/_ ps )
Assertion
Ref Expression
axorbtnotaiffb  |-  -.  ( ph 
<->  ps )

Proof of Theorem axorbtnotaiffb
StepHypRef Expression
1 axorbtnotaiffb.1 . 2  |-  ( ph \/_ ps )
2 df-xor 1296 . . 3  |-  ( (
ph \/_ ps )  <->  -.  ( ph 
<->  ps ) )
32biimpi 186 . 2  |-  ( (
ph \/_ ps )  ->  -.  ( ph  <->  ps )
)
41, 3ax-mp 8 1  |-  -.  ( ph 
<->  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176   \/_wxo 1295
This theorem is referenced by:  axorbciffatcxorb  27873
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-xor 1296
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