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Theorem onunisuci 4119
Description: An ordinal number is equal to the union of its successor. (Contributed by NM, 12-Jun-1994.)
Hypothesis
Ref Expression
on.1  On
Assertion
Ref Expression
onunisuci  U. suc

Proof of Theorem onunisuci
StepHypRef Expression
1 on.1 . . 3  On
21ontrci 4114 . 2  Tr
31elexi 2544 . . 3  _V
43unisuc 4099 . 2  Tr  U. suc
52, 4mpbi 133 1  U. suc
Colors of variables: wff set class
Syntax hints:   wceq 1228   wcel 1374   U.cuni 3554   Tr wtr 3828   Oncon0 4049   suc csuc 4051
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-ral 2289  df-rex 2290  df-v 2537  df-un 2899  df-in 2901  df-ss 2908  df-sn 3356  df-pr 3357  df-uni 3555  df-tr 3829  df-iord 4052  df-on 4054  df-suc 4057
This theorem is referenced by: (None)
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