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Theorem nnsucelrlem4 4427
 Description: Lemma for nnsucelr 4428. Remove and re-adjoin an element to a set. (Contributed by SF, 15-Jan-2015.)
Assertion
Ref Expression
nnsucelrlem4

Proof of Theorem nnsucelrlem4
StepHypRef Expression
1 undif1 3625 . 2
2 snssi 3852 . . 3
3 ssequn2 3436 . . 3
42, 3sylib 188 . 2
51, 4syl5eq 2397 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1642   wcel 1710   cdif 3206   cun 3207   wss 3257  csn 3737 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-ss 3259  df-nul 3551  df-sn 3741 This theorem is referenced by:  nnsucelr  4428  enadj  6060
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