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Theorem pwsn 4243
Description: The power set of a singleton. (Contributed by NM, 5-Jun-2006.)
Assertion
Ref Expression
pwsn

Proof of Theorem pwsn
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sssn 4188 . . 3
21abbii 2591 . 2
3 df-pw 4014 . 2
4 dfpr2 4044 . 2
52, 3, 43eqtr4i 2496 1
Colors of variables: wff setvar class
Syntax hints:  \/wo 368  =wceq 1395  {cab 2442  C_wss 3475   c0 3784  ~Pcpw 4012  {csn 4029  {cpr 4031
This theorem is referenced by:  pmtrsn  16544  topsn  19436  concompid  19932  usgra1v  24390  esumsn  28072  cvmlift2lem9  28756
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-pw 4014  df-sn 4030  df-pr 4032
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