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Theorem ssonunii 4760
Description: The union of a set of ordinal numbers is an ordinal number. Corollary 7N(d) of [Enderton] p. 193. (Contributed by NM, 20-Sep-2003.)
Hypothesis
Ref Expression
ssonuni.1  |-  A  e. 
_V
Assertion
Ref Expression
ssonunii  |-  ( A 
C_  On  ->  U. A  e.  On )

Proof of Theorem ssonunii
StepHypRef Expression
1 ssonuni.1 . 2  |-  A  e. 
_V
2 ssonuni 4759 . 2  |-  ( A  e.  _V  ->  ( A  C_  On  ->  U. A  e.  On ) )
31, 2ax-mp 8 1  |-  ( A 
C_  On  ->  U. A  e.  On )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1725   _Vcvv 2948    C_ wss 3312   U.cuni 4007   Oncon0 4573
This theorem is referenced by:  bm2.5ii  4778  tz9.12lem2  7706  ttukeylem6  8386
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 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395  ax-un 4693
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 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-pss 3328  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-tp 3814  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-tr 4295  df-eprel 4486  df-po 4495  df-so 4496  df-fr 4533  df-we 4535  df-ord 4576  df-on 4577
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