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Theorem sucexg 6630
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 3104 . 2  |-  ( A  e.  V  ->  A  e.  _V )
2 sucexb 6629 . 2  |-  ( A  e.  _V  <->  suc  A  e. 
_V )
31, 2sylib 196 1  |-  ( A  e.  V  ->  suc  A  e.  _V )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    e. wcel 1804   _Vcvv 3095   suc csuc 4870
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-8 1806  ax-9 1808  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421  ax-sep 4558  ax-nul 4566  ax-pr 4676  ax-un 6577
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-ne 2640  df-rex 2799  df-v 3097  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3771  df-sn 4015  df-pr 4017  df-uni 4235  df-suc 4874
This theorem is referenced by:  sucex  6631  suceloni  6633  hsmexlem1  8809  dfon2lem3  29192
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