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Theorem snelpw 4679
 Description: A singleton of a set belongs to the power class of a class containing the set. (Contributed by NM, 1-Apr-1998.)
Hypothesis
Ref Expression
snelpw.1
Assertion
Ref Expression
snelpw

Proof of Theorem snelpw
StepHypRef Expression
1 snelpw.1 . . 3
21snss 4135 . 2
3 snex 4674 . . 3
43elpw 3999 . 2
52, 4bitr4i 252 1
 Colors of variables: wff setvar class Syntax hints:   wb 184   wcel 1802  cvv 3093   wss 3458  cpw 3993  csn 4010 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1603  ax-4 1616  ax-5 1689  ax-6 1732  ax-7 1774  ax-9 1806  ax-10 1821  ax-11 1826  ax-12 1838  ax-13 1983  ax-ext 2419  ax-sep 4554  ax-nul 4562  ax-pr 4672 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 974  df-tru 1384  df-ex 1598  df-nf 1602  df-sb 1725  df-clab 2427  df-cleq 2433  df-clel 2436  df-nfc 2591  df-ne 2638  df-v 3095  df-dif 3461  df-un 3463  df-in 3465  df-ss 3472  df-nul 3768  df-pw 3995  df-sn 4011  df-pr 4013 This theorem is referenced by:  dis2ndc  19827  dislly  19864
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