Home

Metamath Proof Explorer

< Previous   Next > Related theorems Unicode version

---

Theorem p0ex 2760

Description: The power set of the empty set is a set.

Assertion

Ref	Expression
p0ex

---

Proof of Theorem p0ex

Step	Hyp	Ref	Expression
1		snex 2740	1

Colors of variables: wff set class

Syntax hints:   wcel 955  cvv 1802  c0 2270  csn 2399

This theorem is referenced by:  pp0ex 2761  dtru 2762  zfpair 2767  snsn0non 3115  opthprc 3211  fvclex 3841  ensn1 4405  en1 4407  2dom 4408  map1 4411  endisj 4417  pw2en 4426  1sdom2 4505  unxpdom2 4817  sucxpdom 4818  cdavalt 4891  uncdadom 4893  cdaassen 4902  xpcdaen 4903  mapcdaen 4904  cdadom1 4905  axpowndlem3 4923  infxpidmlem9 7503  sn0top 7589

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-11 964  ax-12 965  ax-13 966  ax-14 967  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213  ax-ext 1452  ax-sep 2693  ax-pow 2732

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 978  df-sb 1168  df-eu 1375  df-mo 1376  df-clab 1457  df-cleq 1462  df-clel 1465  df-ne 1579  df-v 1803  df-dif 2039  df-in 2041  df-ss 2043  df-nul 2271  df-pw 2392  df-sn 2402

Copyright terms: Public domain