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Theorem xorexmid 1520
Description: Exclusive-or variant of the law of the excluded middle (exmid 430). 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 (𝜑 ⊻ ¬ 𝜑)

Proof of Theorem xorexmid
StepHypRef Expression
1 pm5.19 374 . 2 ¬ (𝜑 ↔ ¬ 𝜑)
2 df-xor 1505 . 2 ((𝜑 ⊻ ¬ 𝜑) ↔ ¬ (𝜑 ↔ ¬ 𝜑))
31, 2mpbir 221 1 (𝜑 ⊻ ¬ 𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196  wxo 1504
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 197  df-xor 1505
This theorem is referenced by: (None)
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