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Theorem decidi 13016
 Description: Property of being decidable in another class. (Contributed by BJ, 19-Feb-2022.)
Assertion
Ref Expression
decidi DECIDin

Proof of Theorem decidi
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-dcin 13015 . 2 DECIDin DECID
2 df-dc 820 . . . 4 DECID
32ralbii 2441 . . 3 DECID
4 eleq1 2202 . . . . 5
54notbid 656 . . . . 5
64, 5orbi12d 782 . . . 4
76rspccv 2786 . . 3
83, 7sylbi 120 . 2 DECID
91, 8sylbi 120 1 DECIDin
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wo 697  DECID wdc 819   wceq 1331   wcel 1480  wral 2416   DECIDin wdcin 13014 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  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-dc 820  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-v 2688  df-dcin 13015 This theorem is referenced by:  decidin  13018
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