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Theorem dftest 13430
Description: A proposition is testable iff its negative or double-negative is true. See Chapter 2 [Moschovakis] p. 2.

We do not formally define testability with a new token, but instead use DECID ¬ before the formula in question. For example, DECID ¬ 𝑥 = 𝑦 corresponds to "𝑥 = 𝑦 is testable". (Contributed by David A. Wheeler, 13-Aug-2018.) For statements about testable propositions, search for the keyword "testable" in the comments of statements, for instance using the Metamath command "MM> SEARCH * "testable" / COMMENTS". (New usage is discouraged.)

Ref Expression
dftest (DECID ¬ 𝜑 ↔ (¬ 𝜑 ∨ ¬ ¬ 𝜑))

Proof of Theorem dftest
StepHypRef Expression
1 df-dc 821 1 (DECID ¬ 𝜑 ↔ (¬ 𝜑 ∨ ¬ ¬ 𝜑))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 104  wo 698  DECID wdc 820
This theorem depends on definitions:  df-dc 821
This theorem is referenced by: (None)
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