New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  pw0 Unicode version

Theorem pw0 4160
 Description: Compute the power set of the empty set. Theorem 89 of [Suppes] p. 47. (The proof was shortened by Andrew Salmon, 29-Jun-2011.) (Contributed by SF, 5-Aug-1993.) (Revised by SF, 29-Jun-2011.)
Assertion
Ref Expression
pw0

Proof of Theorem pw0
StepHypRef Expression
1 ss0b 3580 . . 3
21abbii 2465 . 2
3 df-pw 3724 . 2
4 df-sn 3741 . 2
52, 3, 43eqtr4i 2383 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1642  cab 2339   wss 3257  c0 3550  cpw 3722  csn 3737 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-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215  df-ss 3259  df-nul 3551  df-pw 3724  df-sn 3741 This theorem is referenced by:  pw10  4161  nnpweq  4523  sfin01  4528
 Copyright terms: Public domain W3C validator