 Mathbox for David A. Wheeler < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  testable Structured version   Visualization version   GIF version

Theorem testable 42314
 Description: In classical logic all wffs are testable, that is, it is always true that (¬ 𝜑 ∨ ¬ ¬ 𝜑). This is not necessarily true in intuitionistic logic. In intuitionistic logic, if this statement is true for some 𝜑, then 𝜑 is testable. The proof is trivial because it's simply a special case of the law of the excluded middle, which is true in classical logic but not necessarily true in intuitionisic logic. (Contributed by David A. Wheeler, 5-Dec-2018.)
Assertion
Ref Expression
testable 𝜑 ∨ ¬ ¬ 𝜑)

Proof of Theorem testable
StepHypRef Expression
1 exmid 429 1 𝜑 ∨ ¬ ¬ 𝜑)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   ∨ wo 381 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 195  df-or 383 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator