Theorem pw0 4177

Description: Compute the power set of the empty set. Theorem 89 of [Suppes] p. 47. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)

Assertion

Ref	Expression
pw0

Proof of Theorem pw0

Step	Hyp	Ref	Expression
1		ss0b 3815	. . 3
2	1	abbii 2591	. 2
3		df-pw 4014	. 2
4		df-sn 4030	. 2
5	2, 3, 4	3eqtr4i 2496	1

Syntax hints:  =wceq 1395  {cab 2442  C_wss 3475  c0 3784  ~Pcpw 4012  {csn 4029

This theorem is referenced by:  p0ex  4639  pwfi  7835  ackbij1lem14  8634  fin1a2lem12  8812  0tsk  9154  hashbc  12502  incexclem  13648  sn0topon  19499  sn0cld  19591  ust0  20722  uhgra0v  24310  usgra0v  24371  esumnul  28059  rankeq1o  29828  ssoninhaus  29913  uhg0v  32377

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-an 371  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-v 3111  df-dif 3478  df-in 3482  df-ss 3489  df-nul 3785  df-pw 4014  df-sn 4030