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Theorem sucex 7514
Description: The successor of a set is a set. (Contributed by NM, 30-Aug-1993.)
Hypothesis
Ref Expression
sucex.1 𝐴 ∈ V
Assertion
Ref Expression
sucex suc 𝐴 ∈ V

Proof of Theorem sucex
StepHypRef Expression
1 sucex.1 . 2 𝐴 ∈ V
2 sucexg 7513 . 2 (𝐴 ∈ V → suc 𝐴 ∈ V)
31, 2ax-mp 5 1 suc 𝐴 ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2107  Vcvv 3500  suc csuc 6191
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2153  ax-12 2169  ax-ext 2798  ax-sep 5200  ax-nul 5207  ax-pr 5326  ax-un 7451
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 844  df-tru 1533  df-ex 1774  df-nf 1778  df-sb 2063  df-clab 2805  df-cleq 2819  df-clel 2898  df-nfc 2968  df-rex 3149  df-rab 3152  df-v 3502  df-dif 3943  df-un 3945  df-in 3947  df-ss 3956  df-nul 4296  df-sn 4565  df-pr 4567  df-uni 4838  df-suc 6195
This theorem is referenced by:  orduninsuc  7546  tfindsg  7563  tfinds2  7566  finds  7596  findsg  7597  finds2  7598  seqomlem1  8077  2oex  8103  oasuc  8140  onasuc  8144  infensuc  8684  phplem4  8688  php  8690  inf0  9073  inf3lem1  9080  dfom3  9099  cantnflt  9124  cantnflem1  9141  cnfcom  9152  infxpenlem  9428  pwsdompw  9615  cfslb2n  9679  cfsmolem  9681  fin1a2lem12  9822  axdc4lem  9866  alephreg  9993  bnj986  32112  bnj1018  32120  satf  32484  dfon2lem7  32918  rdgssun  34528  dford3lem2  39489
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