Theorem ssel2 3023

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 3022	. 2 |- ( A C_ B -> ( C e. A -> C e. B ) )
2	1	imp 123	1 |- ( ( A C_ B /\ C e. A ) -> C e. B )

Syntax hints:   -> wi 4   /\ wa 103   e. wcel 1439   C_ wss 3002

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-11 1443  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071

This theorem depends on definitions:  df-bi 116  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-in 3008  df-ss 3015

This theorem is referenced by:  elnn  4435  funimass4  5370  fvelimab  5375  ssimaex  5380  funconstss  5433  rexima  5550  ralima  5551  1st2nd  5967  f1o2ndf1  6009  tfri1dALT  6132  eldju1st  6818  lbinf  8472  dfinfre  8480  lbzbi  9164  elfzom1elp1fzo  9676  ssfzo12  9698  seq3split  9970  iseqsplit  9971  shftlem  10313  tgcl  11827  neipsm  11917