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Theorem dcdc 9236
Description: Decidability of a proposition is decidable if and only if that proposition is decidable. DECID is idempotent. (Contributed by BJ, 9-Oct-2019.)
Assertion
Ref Expression
dcdc DECID DECID DECID

Proof of Theorem dcdc
StepHypRef Expression
1 df-dc 742 . 2 DECID DECID DECID DECID
2 nndc 9235 . . 3 DECID
32biorfi 664 . 2 DECID DECID DECID
41, 3bitr4i 176 1 DECID DECID DECID
Colors of variables: wff set class
Syntax hints:   wn 3   wb 98   wo 628  DECID wdc 741
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629
This theorem depends on definitions:  df-bi 110  df-dc 742
This theorem is referenced by: (None)
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