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Theorem dcnnOLD 849
Description: Obsolete proof of dcnnOLD 849 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 634 . . . 4  |-  ( -. 
-.  -.  ph  <->  -.  ph )
21orbi2i 762 . . 3  |-  ( ( -.  -.  ph  \/  -.  -.  -.  ph )  <->  ( -.  -.  ph  \/  -.  ph ) )
3 orcom 728 . . 3  |-  ( ( -.  -.  ph  \/  -.  ph )  <->  ( -.  ph  \/  -.  -.  ph ) )
42, 3bitri 184 . 2  |-  ( ( -.  -.  ph  \/  -.  -.  -.  ph )  <->  ( -.  ph  \/  -.  -.  ph ) )
5 df-dc 835 . 2  |-  (DECID  -.  -.  ph  <->  ( -.  -.  ph  \/  -.  -.  -.  ph )
)
6 df-dc 835 . 2  |-  (DECID  -.  ph  <->  ( -.  ph  \/  -.  -.  ph ) )
74, 5, 63bitr4ri 213 1  |-  (DECID  -.  ph  <-> DECID  -.  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 105    \/ wo 708  DECID wdc 834
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-io 709
This theorem depends on definitions:  df-bi 117  df-dc 835
This theorem is referenced by: (None)
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