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Theorem sucssel 4127
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 (A 𝑉 → (suc ABA B))

Proof of Theorem sucssel
StepHypRef Expression
1 sucidg 4119 . 2 (A 𝑉A suc A)
2 ssel 2933 . 2 (suc AB → (A suc AA B))
31, 2syl5com 26 1 (A 𝑉 → (suc ABA B))
Colors of variables: wff set class
Syntax hints:  wi 4   wcel 1390  wss 2911  suc csuc 4068
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-sn 3373  df-suc 4074
This theorem is referenced by:  ordelsuc  4197  bj-nnelirr  9341
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