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Theorem elelpwi 3648
Description: If  A belongs to a part of  C then  A belongs to  C. (Contributed by FL, 3-Aug-2009.)
Assertion
Ref Expression
elelpwi  |-  ( ( A  e.  B  /\  B  e.  ~P C
)  ->  A  e.  C )

Proof of Theorem elelpwi
StepHypRef Expression
1 elpwi 3646 . . 3  |-  ( B  e.  ~P C  ->  B  C_  C )
21sseld 3192 . 2  |-  ( B  e.  ~P C  -> 
( A  e.  B  ->  A  e.  C ) )
32impcom 419 1  |-  ( ( A  e.  B  /\  B  e.  ~P C
)  ->  A  e.  C )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    e. wcel 1696   ~Pcpw 3638
This theorem is referenced by:  unipw  4240  axdc2lem  8090  axdc3lem4  8095  homarel  13884  txdis  17342  ballotlem2  23063  insiga  23513  measinblem  23562  imambfm  23582  totprobd  23644  dstrvprob  23687  bwt2  25695
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-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
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-v 2803  df-in 3172  df-ss 3179  df-pw 3640
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