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Theorem ordunisuc2r 4467
 Description: An ordinal which contains the successor of each of its members is equal to its union. (Contributed by Jim Kingdon, 14-Nov-2018.)
Assertion
Ref Expression
ordunisuc2r
Distinct variable group:   ,

Proof of Theorem ordunisuc2r
StepHypRef Expression
1 vex 2712 . . . . . . . . 9
21sucid 4372 . . . . . . . 8
3 elunii 3773 . . . . . . . 8
42, 3mpan 421 . . . . . . 7
54imim2i 12 . . . . . 6
65alimi 1432 . . . . 5
7 df-ral 2437 . . . . 5
8 dfss2 3113 . . . . 5
96, 7, 83imtr4i 200 . . . 4
109a1i 9 . . 3
11 orduniss 4380 . . 3
1210, 11jctird 315 . 2
13 eqss 3139 . 2
1412, 13syl6ibr 161 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103  wal 1330   wceq 1332   wcel 2125  wral 2432   wss 3098  cuni 3768   word 4317   csuc 4320 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 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-ral 2437  df-v 2711  df-un 3102  df-in 3104  df-ss 3111  df-sn 3562  df-uni 3769  df-tr 4059  df-iord 4321  df-suc 4326 This theorem is referenced by: (None)
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