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Theorem sucex 6627
Description: The successor of a set is a set. (Contributed by NM, 30-Aug-1993.)
Hypothesis
Ref Expression
sucex.1  |-  A  e. 
_V
Assertion
Ref Expression
sucex  |-  suc  A  e.  _V

Proof of Theorem sucex
StepHypRef Expression
1 sucex.1 . 2  |-  A  e. 
_V
2 sucexg 6626 . 2  |-  ( A  e.  _V  ->  suc  A  e.  _V )
31, 2ax-mp 5 1  |-  suc  A  e.  _V
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1802   _Vcvv 3093   suc csuc 4866
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1603  ax-4 1616  ax-5 1689  ax-6 1732  ax-7 1774  ax-8 1804  ax-9 1806  ax-10 1821  ax-11 1826  ax-12 1838  ax-13 1983  ax-ext 2419  ax-sep 4554  ax-nul 4562  ax-pr 4672  ax-un 6573
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1384  df-ex 1598  df-nf 1602  df-sb 1725  df-clab 2427  df-cleq 2433  df-clel 2436  df-nfc 2591  df-ne 2638  df-rex 2797  df-v 3095  df-dif 3461  df-un 3463  df-in 3465  df-ss 3472  df-nul 3768  df-sn 4011  df-pr 4013  df-uni 4231  df-suc 4870
This theorem is referenced by:  orduninsuc  6659  tfindsg  6676  tfinds2  6679  finds  6707  findsg  6708  finds2  6709  seqomlem1  7113  oasuc  7172  onasuc  7176  infensuc  7693  phplem4  7697  php  7699  inf0  8036  inf3lem1  8043  dfom3  8062  cantnflt  8089  cantnflem1  8106  cantnfltOLD  8119  cantnflem1OLD  8129  cnfcom  8142  cnfcomOLD  8150  infxpenlem  8389  pwsdompw  8582  ackbij1lem5  8602  cfslb2n  8646  cfsmolem  8648  fin1a2lem12  8789  axdc4lem  8833  alephreg  8955  dfon2lem7  29189  dford3lem2  30937  bnj986  33719  bnj1018  33727  bj-1ex  34219  bj-2ex  34220
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