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Mirrors > Home > MPE Home > Th. List > Mathboxes > testable | Structured version Visualization version GIF version |
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.) |
Ref | Expression |
---|---|
testable | ⊢ (¬ 𝜑 ∨ ¬ ¬ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exmid 891 | 1 ⊢ (¬ 𝜑 ∨ ¬ ¬ 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∨ wo 843 |
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 209 df-or 844 |
This theorem is referenced by: (None) |
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