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Theorem sucex 4618
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 4617 . 2  |-  ( A  e.  _V  ->  suc  A  e.  _V )
31, 2ax-mp 8 1  |-  suc  A  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1696   _Vcvv 2801   suc csuc 4410
This theorem is referenced by:  orduninsuc  4650  tfindsg  4667  tfinds2  4670  finds  4698  findsg  4699  finds2  4700  seqomlem1  6478  oasuc  6539  onasuc  6543  infensuc  7055  phplem4  7059  php  7061  inf0  7338  inf3lem1  7345  dfom3  7364  cantnflt  7389  cantnflem1  7407  cnfcom  7419  infxpenlem  7657  pwsdompw  7846  ackbij1lem5  7866  cfslb2n  7910  cfsmolem  7912  fin1a2lem12  8053  axdc4lem  8097  alephreg  8220  dfon2lem7  24216  dford3lem2  27223  bnj986  29302  bnj1018  29310
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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