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Theorem elelpwi 3635
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 3633 . . 3  |-  ( B  e.  ~P C  ->  B  C_  C )
21sseld 3179 . 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 1684   ~Pcpw 3625
This theorem is referenced by:  unipw  4224  axdc2lem  8074  axdc3lem4  8079  homarel  13868  txdis  17326  ballotlem2  23047  insiga  23498  measinblem  23547  imambfm  23567  totprobd  23629  dstrvprob  23672  bwt2  25592
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-in 3159  df-ss 3166  df-pw 3627
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