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Theorem rabxmdc 3400
 Description: Law of excluded middle given decidability, in terms of restricted class abstractions. (Contributed by Jim Kingdon, 2-Aug-2018.)
Assertion
Ref Expression
rabxmdc DECID
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem rabxmdc
StepHypRef Expression
1 exmiddc 822 . . . . . 6 DECID
21a1d 22 . . . . 5 DECID
32alimi 1432 . . . 4 DECID
4 df-ral 2422 . . . 4
53, 4sylibr 133 . . 3 DECID
6 rabid2 2611 . . 3
75, 6sylibr 133 . 2 DECID
8 unrab 3353 . 2
97, 8eqtr4di 2191 1 DECID
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wo 698  DECID wdc 820  wal 1330   wceq 1332   wcel 1481  wral 2417  crab 2421   cun 3075 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-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-dc 821  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-rab 2426  df-v 2692  df-un 3081 This theorem is referenced by: (None)
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