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Theorem sucexg 4730
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 2907 . 2  |-  ( A  e.  V  ->  A  e.  _V )
2 sucexb 4729 . 2  |-  ( A  e.  _V  <->  suc  A  e. 
_V )
31, 2sylib 189 1  |-  ( A  e.  V  ->  suc  A  e.  _V )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1717   _Vcvv 2899   suc csuc 4524
This theorem is referenced by:  sucex  4731  suceloni  4733  hsmexlem1  8239  dfon2lem3  25165
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-13 1719  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368  ax-sep 4271  ax-nul 4279  ax-pr 4344  ax-un 4641
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-ne 2552  df-rex 2655  df-v 2901  df-dif 3266  df-un 3268  df-in 3270  df-ss 3277  df-nul 3572  df-sn 3763  df-pr 3764  df-uni 3958  df-suc 4528
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