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Theorem elelpwi 3576
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 3573 . . 3  |-  ( B  e.  ~P C  ->  B  C_  C )
21sseld 3146 . 2  |-  ( B  e.  ~P C  -> 
( A  e.  B  ->  A  e.  C ) )
32impcom 124 1  |-  ( ( A  e.  B  /\  B  e.  ~P C
)  ->  A  e.  C )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    e. wcel 2141   ~Pcpw 3564
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-in 3127  df-ss 3134  df-pw 3566
This theorem is referenced by:  unipw  4200  txdis  13036
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