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Theorem sucexg 4617
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 2809 . 2  |-  ( A  e.  V  ->  A  e.  _V )
2 sucexb 4616 . 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 1696   _Vcvv 2801   suc csuc 4410
This theorem is referenced by:  sucex  4618  suceloni  4620  hsmexlem1  8068  dfon2lem3  24212
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-13 1698  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230  ax-un 4528
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-rex 2562  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-sn 3659  df-pr 3660  df-uni 3844  df-suc 4414
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