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Theorem ssonunii 4551
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 4550 . 2  |-  ( A  e.  _V  ->  ( A  C_  On  ->  U. A  e.  On ) )
31, 2ax-mp 10 1  |-  ( A 
C_  On  ->  U. A  e.  On )
Colors of variables: wff set class
Syntax hints:    -> wi 6    e. wcel 1621   _Vcvv 2763    C_ wss 3127   U.cuni 3801   Oncon0 4364
This theorem is referenced by:  bm2.5ii  4569  tz9.12lem2  7428  ttukeylem6  8109
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-13 1625  ax-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927  ax-ext 2239  ax-sep 4115  ax-nul 4123  ax-pr 4186  ax-un 4484
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3or 940  df-3an 941  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-eu 2122  df-mo 2123  df-clab 2245  df-cleq 2251  df-clel 2254  df-nfc 2383  df-ne 2423  df-ral 2523  df-rex 2524  df-rab 2527  df-v 2765  df-sbc 2967  df-dif 3130  df-un 3132  df-in 3134  df-ss 3141  df-pss 3143  df-nul 3431  df-if 3540  df-sn 3620  df-pr 3621  df-tp 3622  df-op 3623  df-uni 3802  df-br 3998  df-opab 4052  df-tr 4088  df-eprel 4277  df-po 4286  df-so 4287  df-fr 4324  df-we 4326  df-ord 4367  df-on 4368
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