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Theorem dftest 13168
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.)

Assertion
Ref Expression
dftest  |-  (DECID  -.  ph  <->  ( -.  ph  \/  -.  -.  ph ) )

Proof of Theorem dftest
StepHypRef Expression
1 df-dc 805 1  |-  (DECID  -.  ph  <->  ( -.  ph  \/  -.  -.  ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 104    \/ wo 682  DECID wdc 804
This theorem depends on definitions:  df-dc 805
This theorem is referenced by: (None)
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