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Theorem sucexg 4601
Description: The successor of a set is a set (generalization). (Contributed by NM, 5-Jun-1994.)
Assertion
Ref Expression
sucexg  |-  ( A  e.  V  ->  suc  A  e.  _V )

Proof of Theorem sucexg
StepHypRef Expression
1 elex 2796 . 2  |-  ( A  e.  V  ->  A  e.  _V )
2 sucexb 4600 . 2  |-  ( A  e.  _V  <->  suc  A  e. 
_V )
31, 2sylib 188 1  |-  ( A  e.  V  ->  suc  A  e.  _V )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1684   _Vcvv 2788   suc csuc 4394
This theorem is referenced by:  sucex  4602  suceloni  4604  hsmexlem1  8052  dfon2lem3  24141
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-13 1686  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214  ax-un 4512
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-rex 2549  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-sn 3646  df-pr 3647  df-uni 3828  df-suc 4398
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