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Theorem xorexmid 1376
Description: Exclusive-or variant of the law of the excluded middle (exmid 415). This statement is ancient, going back to at least Stoic logic. This statement does not necessarily hold in intuitionistic logic. (Contributed by David A. Wheeler, 23-Feb-2019.)
Assertion
Ref Expression
xorexmid  |-  ( ph  \/_ 
-.  ph )

Proof of Theorem xorexmid
StepHypRef Expression
1 pm5.19 360 . 2  |-  -.  ( ph 
<->  -.  ph )
2 df-xor 1361 . 2  |-  ( (
ph  \/_  -.  ph )  <->  -.  ( ph  <->  -.  ph )
)
31, 2mpbir 209 1  |-  ( ph  \/_ 
-.  ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184    \/_ wxo 1360
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-xor 1361
This theorem is referenced by: (None)
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