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Theorem sucssel 4975
 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 4961 . 2
2 ssel 3497 . 2
31, 2syl5com 30 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  e.wcel 1818  C_wss 3475  succsuc 4885 This theorem is referenced by:  suc11  4986  ordelsuc  6655  ordsucelsuc  6657  oaordi  7214  nnaordi  7286  unbnn2  7797  ackbij1b  8640  ackbij2  8644  cflm  8651  isf32lem2  8755  indpi  9306  dfon2lem3  29217 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-un 3480  df-in 3482  df-ss 3489  df-sn 4030  df-suc 4889
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