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Theorem sucssel 4666
 Description: A set whose successor is a subset of another class is a member of that class. (Contributed by NM, 16-Sep-1995.)
Assertion
Ref Expression
sucssel

Proof of Theorem sucssel
StepHypRef Expression
1 sucidg 4651 . 2
2 ssel 3334 . 2
31, 2syl5com 28 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1725   wss 3312   csuc 4575 This theorem is referenced by:  suc11  4677  ordelsuc  4792  ordsucelsuc  4794  oaordi  6781  nnaordi  6853  unbnn2  7356  ackbij1b  8111  ackbij2  8115  cflm  8122  isf32lem2  8226  indpi  8776  dfon2lem3  25404 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-un 3317  df-in 3319  df-ss 3326  df-sn 3812  df-suc 4579
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