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Theorem elelpwi 3809
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 3807 . . 3  |-  ( B  e.  ~P C  ->  B  C_  C )
21sseld 3347 . 2  |-  ( B  e.  ~P C  -> 
( A  e.  B  ->  A  e.  C ) )
32impcom 420 1  |-  ( ( A  e.  B  /\  B  e.  ~P C
)  ->  A  e.  C )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359    e. wcel 1725   ~Pcpw 3799
This theorem is referenced by:  unipw  4414  axdc2lem  8328  axdc3lem4  8333  homarel  14191  bwth  17473  txdis  17664  insiga  24520  measinblem  24574  imambfm  24612  totprobd  24684  dstrvprob  24729  ballotlem2  24746
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-in 3327  df-ss 3334  df-pw 3801
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