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Theorem snelpwi 4129
 Description: A singleton of a set belongs to the power class of a class containing the set. (Contributed by Alan Sare, 25-Aug-2011.)
Assertion
Ref Expression
snelpwi

Proof of Theorem snelpwi
StepHypRef Expression
1 snssi 3659 . 2
2 elex 2692 . . 3
3 snexg 4103 . . 3
4 elpwg 3513 . . 3
52, 3, 43syl 17 . 2
61, 5mpbird 166 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wcel 1480  cvv 2681   wss 3066  cpw 3505  csn 3522 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119  ax-sep 4041  ax-pow 4093 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-in 3072  df-ss 3079  df-pw 3507  df-sn 3528 This theorem is referenced by:  unipw  4134  infpwfidom  7047  txdis  12435  txdis1cn  12436
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