Users' Mathboxes Mathbox for David A. Wheeler < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  dftest Unicode version

Theorem dftest 13951
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 825 1  |-  (DECID  -.  ph  <->  ( -.  ph  \/  -.  -.  ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 104    \/ wo 698  DECID wdc 824
This theorem depends on definitions:  df-dc 825
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator