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Theorem setind2 4369
 Description: Set (epsilon) induction, stated compactly. Given as a homework problem in 1992 by George Boolos (1940-1996). (Contributed by NM, 17-Sep-2003.)
Assertion
Ref Expression
setind2

Proof of Theorem setind2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 pwss 3449 . 2
2 setind 4368 . 2
31, 2sylbi 120 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1288   wceq 1290   wcel 1439  cvv 2620   wss 3000  cpw 3433 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071  ax-setind 4366 This theorem depends on definitions:  df-bi 116  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-ral 2365  df-v 2622  df-in 3006  df-ss 3013  df-pw 3435 This theorem is referenced by: (None)
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