New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  pwpwpw0 Unicode version

Theorem pwpwpw0 3885
 Description: Compute the power set of the power set of the power set of the empty set. (See also pw0 4160 and pwpw0 3855.) (Contributed by NM, 2-May-2009.)
Assertion
Ref Expression
pwpwpw0

Proof of Theorem pwpwpw0
StepHypRef Expression
1 pwpr 3883 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1642   cun 3207  c0 3550  cpw 3722  csn 3737  cpr 3738 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-ral 2619  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-ss 3259  df-nul 3551  df-pw 3724  df-sn 3741  df-pr 3742 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator