Theorem ssel2 2994

Description: Membership relationships follow from a subclass relationship. (Contributed by NM, 7-Jun-2004.)

Assertion

Ref	Expression
ssel2	|- ( ( A C_ B /\ C e. A ) -> C e. B )

Proof of Theorem ssel2

Step	Hyp	Ref	Expression
1		ssel 2993	. 2 |- ( A C_ B -> ( C e. A -> C e. B ) )
2	1	imp 122	1 |- ( ( A C_ B /\ C e. A ) -> C e. B )

Syntax hints:   -> wi 4   /\ wa 102   e. wcel 1433   C_ wss 2973

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-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-11 1437  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-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-in 2979  df-ss 2986

This theorem is referenced by:  elnn  4346  funimass4  5245  fvelimab  5250  ssimaex  5255  funconstss  5306  rexima  5415  ralima  5416  1st2nd  5827  f1o2ndf1  5869  lbinf  8026  dfinfre  8034  lbzbi  8701  elfzom1elp1fzo  9211  ssfzo12  9233  iseqsplit  9458  shftlem  9704