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Theorem xorexmid 1649
Description: Exclusive-or variant of the law of the excluded middle (exmid 918). 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 pm5.19 376 . 2 ¬ (𝜑 ↔ ¬ 𝜑)
2 df-xor 1634 . 2 ((𝜑 ⊻ ¬ 𝜑) ↔ ¬ (𝜑 ↔ ¬ 𝜑))
31, 2mpbir 222 1 (𝜑 ⊻ ¬ 𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 197  wxo 1633
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 198  df-xor 1634
This theorem is referenced by: (None)
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