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Theorem dcnnOLD 839
Description: Obsolete proof of dcnnOLD 839 as of 25-Nov-2023. (Contributed by David A. Wheeler, 6-Dec-2018.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
dcnnOLD  |-  (DECID  -.  ph  <-> DECID  -.  -.  ph )

Proof of Theorem dcnnOLD
StepHypRef Expression
1 notnotnot 624 . . . 4  |-  ( -. 
-.  -.  ph  <->  -.  ph )
21orbi2i 752 . . 3  |-  ( ( -.  -.  ph  \/  -.  -.  -.  ph )  <->  ( -.  -.  ph  \/  -.  ph ) )
3 orcom 718 . . 3  |-  ( ( -.  -.  ph  \/  -.  ph )  <->  ( -.  ph  \/  -.  -.  ph ) )
42, 3bitri 183 . 2  |-  ( ( -.  -.  ph  \/  -.  -.  -.  ph )  <->  ( -.  ph  \/  -.  -.  ph ) )
5 df-dc 825 . 2  |-  (DECID  -.  -.  ph  <->  ( -.  -.  ph  \/  -.  -.  -.  ph )
)
6 df-dc 825 . 2  |-  (DECID  -.  ph  <->  ( -.  ph  \/  -.  -.  ph ) )
74, 5, 63bitr4ri 212 1  |-  (DECID  -.  ph  <-> DECID  -.  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 104    \/ wo 698  DECID wdc 824
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699
This theorem depends on definitions:  df-bi 116  df-dc 825
This theorem is referenced by: (None)
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