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Theorem ssonuni 4753
 Description: The union of a set of ordinal numbers is an ordinal number. Theorem 9 of [Suppes] p. 132. (Contributed by NM, 1-Nov-2003.)
Assertion
Ref Expression
ssonuni

Proof of Theorem ssonuni
StepHypRef Expression
1 ssorduni 4752 . 2
2 uniexg 4692 . . 3
3 elong 4576 . . 3
42, 3syl 16 . 2
51, 4syl5ibr 213 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wcel 1725  cvv 2943   wss 3307  cuni 4002   word 4567  con0 4568 This theorem is referenced by:  ssonunii  4754  onuni  4759  iunon  6586  onfununi  6589  oemapvali  7624  cardprclem  7850  carduni  7852  dfac12lem2  8008  ontgval  26124 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2411  ax-sep 4317  ax-nul 4325  ax-pr 4390  ax-un 4687 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2417  df-cleq 2423  df-clel 2426  df-nfc 2555  df-ne 2595  df-ral 2697  df-rex 2698  df-rab 2701  df-v 2945  df-sbc 3149  df-dif 3310  df-un 3312  df-in 3314  df-ss 3321  df-pss 3323  df-nul 3616  df-if 3727  df-sn 3807  df-pr 3808  df-tp 3809  df-op 3810  df-uni 4003  df-br 4200  df-opab 4254  df-tr 4290  df-eprel 4481  df-po 4490  df-so 4491  df-fr 4528  df-we 4530  df-ord 4571  df-on 4572
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