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Theorem sucexg 4782
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 2956 . 2  |-  ( A  e.  V  ->  A  e.  _V )
2 sucexb 4781 . 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 1725   _Vcvv 2948   suc csuc 4575
This theorem is referenced by:  sucex  4783  suceloni  4785  hsmexlem1  8298  dfon2lem3  25404
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-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-rex 2703  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-sn 3812  df-pr 3813  df-uni 4008  df-suc 4579
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