Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  unipwrVD Unicode version

Theorem unipwrVD 28924
Description: Virtual deduction proof of unipwr 28925. (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 2804 . . . . 5  |-  x  e. 
_V
21snid 3680 . . . 4  |-  x  e. 
{ x }
3 idn1 28641 . . . . 5  |-  (. x  e.  A  ->.  x  e.  A ).
4 snelpwi 4236 . . . . 5  |-  ( x  e.  A  ->  { x }  e.  ~P A
)
53, 4e1_ 28704 . . . 4  |-  (. x  e.  A  ->.  { x }  e.  ~P A ).
6 elunii 3848 . . . 4  |-  ( ( x  e.  { x }  /\  { x }  e.  ~P A )  ->  x  e.  U. ~P A
)
72, 5, 6e01an 28770 . . 3  |-  (. x  e.  A  ->.  x  e.  U. ~P A ).
87in1 28638 . 2  |-  ( x  e.  A  ->  x  e.  U. ~P A )
98ssriv 3197 1  |-  A  C_  U. ~P A
Colors of variables: wff set class
Syntax hints:    e. wcel 1696    C_ wss 3165   ~Pcpw 3638   {csn 3653   U.cuni 3843
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-pr 4230
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-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-pw 3640  df-sn 3659  df-pr 3660  df-uni 3844  df-vd1 28637
  Copyright terms: Public domain W3C validator