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Theorem unipwrVD 28945
Description: Virtual deduction proof of unipwr 28946. (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 2960 . . . . 5  |-  x  e. 
_V
21snid 3842 . . . 4  |-  x  e. 
{ x }
3 idn1 28666 . . . . 5  |-  (. x  e.  A  ->.  x  e.  A ).
4 snelpwi 4410 . . . . 5  |-  ( x  e.  A  ->  { x }  e.  ~P A
)
53, 4e1_ 28729 . . . 4  |-  (. x  e.  A  ->.  { x }  e.  ~P A ).
6 elunii 4021 . . . 4  |-  ( ( x  e.  { x }  /\  { x }  e.  ~P A )  ->  x  e.  U. ~P A
)
72, 5, 6e01an 28794 . . 3  |-  (. x  e.  A  ->.  x  e.  U. ~P A ).
87in1 28663 . 2  |-  ( x  e.  A  ->  x  e.  U. ~P A )
98ssriv 3353 1  |-  A  C_  U. ~P A
Colors of variables: wff set class
Syntax hints:    e. wcel 1726    C_ wss 3321   ~Pcpw 3800   {csn 3815   U.cuni 4016
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418  ax-sep 4331  ax-nul 4339  ax-pr 4404
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ne 2602  df-v 2959  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-nul 3630  df-pw 3802  df-sn 3821  df-pr 3822  df-uni 4017  df-vd1 28662
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