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Theorem rabxmdc 3277
 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 755 . . . . . 6 DECID
21a1d 22 . . . . 5 DECID
32alimi 1360 . . . 4 DECID
4 df-ral 2328 . . . 4
53, 4sylibr 141 . . 3 DECID
6 rabid2 2503 . . 3
75, 6sylibr 141 . 2 DECID
8 unrab 3236 . 2
97, 8syl6eqr 2106 1 DECID
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wo 639  DECID wdc 753  wal 1257   wceq 1259   wcel 1409  wral 2323  crab 2327   cun 2943 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-dc 754  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328  df-rab 2332  df-v 2576  df-un 2950 This theorem is referenced by: (None)
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