Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  onsucuni Unicode version

Theorem onsucuni 4775
 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 4733 . 2
2 ssid 3335 . . 3
3 ordunisssuc 4651 . . 3
42, 3mpbii 203 . 2
51, 4mpdan 650 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wss 3288  cuni 3983   word 4548  con0 4549   csuc 4551 This theorem is referenced by:  ordsucuni  4776  tz9.12lem3  7679  onssnum  7885  dfac12lem2  7988  ackbij1lem16  8079  cfslb2n  8112  hsmexlem1  8270 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-13 1723  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393  ax-sep 4298  ax-nul 4306  ax-pr 4371  ax-un 4668 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2266  df-mo 2267  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-ne 2577  df-ral 2679  df-rex 2680  df-rab 2683  df-v 2926  df-sbc 3130  df-dif 3291  df-un 3293  df-in 3295  df-ss 3302  df-pss 3304  df-nul 3597  df-if 3708  df-sn 3788  df-pr 3789  df-tp 3790  df-op 3791  df-uni 3984  df-br 4181  df-opab 4235  df-tr 4271  df-eprel 4462  df-po 4471  df-so 4472  df-fr 4509  df-we 4511  df-ord 4552  df-on 4553  df-suc 4555
 Copyright terms: Public domain W3C validator