MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  snelpw Unicode version

Theorem snelpw 4655
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 4116 . 2
3 snex 4650 . . 3
43elpw 3982 . 2
52, 4bitr4i 252 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  e.wcel 1758   cvv 3081  C_wss 3442  ~Pcpw 3976  {csn 3993
This theorem is referenced by:  dis2ndc  19463  dislly  19500
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432  ax-sep 4530  ax-nul 4538  ax-pr 4648
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-v 3083  df-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3752  df-pw 3978  df-sn 3994  df-pr 3996
  Copyright terms: Public domain W3C validator