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Theorem onsucuni 6663
Description: A class of ordinal numbers is a subclass of the successor of its union. Similar to Proposition 7.26 of [TakeutiZaring] p. 41. (Contributed by NM, 19-Sep-2003.)
Assertion
Ref Expression
onsucuni

Proof of Theorem onsucuni
StepHypRef Expression
1 ssorduni 6621 . 2
2 ssid 3522 . . 3
3 ordunisssuc 4985 . . 3
42, 3mpbii 211 . 2
51, 4mpdan 668 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  C_wss 3475  U.cuni 4249  Ordword 4882   con0 4883  succsuc 4885
This theorem is referenced by:  ordsucuni  6664  tz9.12lem3  8228  onssnum  8442  dfac12lem2  8545  ackbij1lem16  8636  cfslb2n  8669  hsmexlem1  8827
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-8 1820  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691  ax-un 6592
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 974  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-pss 3491  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-tp 4034  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-tr 4546  df-eprel 4796  df-po 4805  df-so 4806  df-fr 4843  df-we 4845  df-ord 4886  df-on 4887  df-suc 4889
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