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Theorem ordsucuni 4809
Description: An ordinal class is a subclass of the successor of its union. (Contributed by NM, 12-Sep-2003.)
Assertion
Ref Expression
ordsucuni  |-  ( Ord 
A  ->  A  C_  suc  U. A )

Proof of Theorem ordsucuni
StepHypRef Expression
1 ordsson 4770 . 2  |-  ( Ord 
A  ->  A  C_  On )
2 onsucuni 4808 . 2  |-  ( A 
C_  On  ->  A  C_  suc  U. A )
31, 2syl 16 1  |-  ( Ord 
A  ->  A  C_  suc  U. A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    C_ wss 3320   U.cuni 4015   Ord word 4580   Oncon0 4581   suc csuc 4583
This theorem is referenced by:  orduniorsuc  4810
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 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403  ax-un 4701
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 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-pss 3336  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-tp 3822  df-op 3823  df-uni 4016  df-br 4213  df-opab 4267  df-tr 4303  df-eprel 4494  df-po 4503  df-so 4504  df-fr 4541  df-we 4543  df-ord 4584  df-on 4585  df-suc 4587
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