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Theorem unipwrVD 33365
Description: Virtual deduction proof of unipwr 33366. (Contributed by Alan Sare, 25-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
unipwrVD  |-  A  C_  U. ~P A

Proof of Theorem unipwrVD
Dummy variable  x is distinct from all other variables.
StepHypRef Expression
1 vex 3098 . . . . 5  |-  x  e. 
_V
21snid 4042 . . . 4  |-  x  e. 
{ x }
3 idn1 33084 . . . . 5  |-  (. x  e.  A  ->.  x  e.  A ).
4 snelpwi 4682 . . . . 5  |-  ( x  e.  A  ->  { x }  e.  ~P A
)
53, 4e1a 33146 . . . 4  |-  (. x  e.  A  ->.  { x }  e.  ~P A ).
6 elunii 4239 . . . 4  |-  ( ( x  e.  { x }  /\  { x }  e.  ~P A )  ->  x  e.  U. ~P A
)
72, 5, 6e01an 33211 . . 3  |-  (. x  e.  A  ->.  x  e.  U. ~P A ).
87in1 33081 . 2  |-  ( x  e.  A  ->  x  e.  U. ~P A )
98ssriv 3493 1  |-  A  C_  U. ~P A
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1804    C_ wss 3461   ~Pcpw 3997   {csn 4014   U.cuni 4234
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-9 1808  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421  ax-sep 4558  ax-nul 4566  ax-pr 4676
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 976  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-ne 2640  df-v 3097  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3771  df-pw 3999  df-sn 4015  df-pr 4017  df-uni 4235  df-vd1 33080
This theorem is referenced by: (None)
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