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Theorem sucex 6958
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 6957 . 2 (𝐴 ∈ V → suc 𝐴 ∈ V)
31, 2ax-mp 5 1 suc 𝐴 ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 1987  Vcvv 3186  suc csuc 5684
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-8 1989  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601  ax-sep 4741  ax-nul 4749  ax-pr 4867  ax-un 6902
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-rex 2913  df-v 3188  df-dif 3558  df-un 3560  df-in 3562  df-ss 3569  df-nul 3892  df-sn 4149  df-pr 4151  df-uni 4403  df-suc 5688
This theorem is referenced by:  orduninsuc  6990  tfindsg  7007  tfinds2  7010  finds  7039  findsg  7040  finds2  7041  seqomlem1  7490  oasuc  7549  onasuc  7553  infensuc  8082  phplem4  8086  php  8088  inf0  8462  inf3lem1  8469  dfom3  8488  cantnflt  8513  cantnflem1  8530  cnfcom  8541  infxpenlem  8780  pwsdompw  8970  ackbij1lem5  8990  cfslb2n  9034  cfsmolem  9036  fin1a2lem12  9177  axdc4lem  9221  alephreg  9348  bnj986  30729  bnj1018  30737  dfon2lem7  31392  bj-1ex  32582  bj-2ex  32583  dford3lem2  37071
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