MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  p0exALT Unicode version

Theorem p0exALT 4214
Description: The power set of the empty set (the ordinal 1) is a set. Alternate proof which is longer and quite different from the proof of p0ex 4213 if snexALT 4212 is expanded. (Contributed by NM, 23-Dec-1993.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
p0exALT  |-  { (/) }  e.  _V

Proof of Theorem p0exALT
StepHypRef Expression
1 snexALT 4212 1  |-  { (/) }  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1696   _Vcvv 2801   (/)c0 3468   {csn 3653
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pow 4204
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-v 2803  df-dif 3168  df-in 3172  df-ss 3179  df-nul 3469  df-pw 3640  df-sn 3659
  Copyright terms: Public domain W3C validator