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Theorem dfrex2dc 2428
 Description: Relationship between restricted universal and existential quantifiers. (Contributed by Jim Kingdon, 29-Jun-2022.)
Assertion
Ref Expression
dfrex2dc DECID

Proof of Theorem dfrex2dc
StepHypRef Expression
1 df-rex 2422 . . . 4
21dcbii 825 . . 3 DECID DECID
3 dfexdc 1477 . . 3 DECID
42, 3sylbi 120 . 2 DECID
5 df-ral 2421 . . . 4
6 imnan 679 . . . . 5
76albii 1446 . . . 4
85, 7bitri 183 . . 3
98notbii 657 . 2
104, 1, 93bitr4g 222 1 DECID
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 103   wb 104  DECID wdc 819  wal 1329  wex 1468   wcel 1480  wral 2416  wrex 2417 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-gen 1425  ax-ie2 1470 This theorem depends on definitions:  df-bi 116  df-dc 820  df-tru 1334  df-fal 1337  df-ral 2421  df-rex 2422 This theorem is referenced by:  dfrex2fin  6800  exmidomniim  7016
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