Theorem elelpwi 3393

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

Step	Hyp	Ref	Expression
1		elpwi 3391	. . 3 |- ( B e. ~P C -> B C_ C )
2	1	sseld 2998	. 2 |- ( B e. ~P C -> ( A e. B -> A e. C ) )
3	2	impcom 123	1 |- ( ( A e. B /\ B e. ~P C ) -> A e. C )

Syntax hints:   -> wi 4   /\ wa 102   e. wcel 1433   ~Pcpw 3382

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-v 2603  df-in 2979  df-ss 2986  df-pw 3384

This theorem is referenced by:  unipw  3972