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Theorem dcbii 785
Description: The equivalent of a decidable proposition is decidable. (Contributed by Jim Kingdon, 28-Mar-2018.)
Hypothesis
Ref Expression
dcbii.1  |-  ( ph  <->  ps )
Assertion
Ref Expression
dcbii  |-  (DECID  ph  <-> DECID  ps )

Proof of Theorem dcbii
StepHypRef Expression
1 dcbii.1 . . 3  |-  ( ph  <->  ps )
21notbii 629 . . 3  |-  ( -. 
ph 
<->  -.  ps )
31, 2orbi12i 716 . 2  |-  ( (
ph  \/  -.  ph )  <->  ( ps  \/  -.  ps ) )
4 df-dc 781 . 2  |-  (DECID  ph  <->  ( ph  \/  -.  ph ) )
5 df-dc 781 . 2  |-  (DECID  ps  <->  ( ps  \/  -.  ps ) )
63, 4, 53bitr4i 210 1  |-  (DECID  ph  <-> DECID  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 103    \/ wo 664  DECID wdc 780
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-io 665
This theorem depends on definitions:  df-bi 115  df-dc 781
This theorem is referenced by:  dcbi  882  dcned  2261  dfrex2dc  2371  euxfr2dc  2798  exmidexmid  4022  exfzdc  9616  nninfsellemdc  11559
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