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Theorem bj-nndcALT 12948
Description: Alternate proof of nndc 836. (Proof modification is discouraged.) (New usage is discouraged.) (Contributed by BJ, 9-Oct-2019.)
Assertion
Ref Expression
bj-nndcALT  |-  -.  -. DECID  ph

Proof of Theorem bj-nndcALT
StepHypRef Expression
1 notnot 618 . . 3  |-  ( -. 
ph  ->  -.  -.  -.  ph )
2 bj-nnor 12931 . . 3  |-  ( -. 
-.  ( ph  \/  -.  ph )  <->  ( -.  ph 
->  -.  -.  -.  ph ) )
31, 2mpbir 145 . 2  |-  -.  -.  ( ph  \/  -.  ph )
4 df-dc 820 . . 3  |-  (DECID  ph  <->  ( ph  \/  -.  ph ) )
54notbii 657 . 2  |-  ( -. DECID  ph  <->  -.  ( ph  \/  -.  ph ) )
63, 5mtbir 660 1  |-  -.  -. DECID  ph
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 697  DECID wdc 819
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 603  ax-in2 604  ax-io 698
This theorem depends on definitions:  df-bi 116  df-dc 820
This theorem is referenced by: (None)
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