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Theorem p0exALT 4379
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 4378 if snexALT 4377 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 4377 1  |-  { (/) }  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1725   _Vcvv 2948   (/)c0 3620   {csn 3806
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pow 4369
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-v 2950  df-dif 3315  df-in 3319  df-ss 3326  df-nul 3621  df-pw 3793  df-sn 3812
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