Theorem ssel2 3219

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 3218	. 2 |- ( A C_ B -> ( C e. A -> C e. B ) )
2	1	imp 124	1 |- ( ( A C_ B /\ C e. A ) -> C e. B )

Syntax hints:   -> wi 4   /\ wa 104   e. wcel 2200   C_ wss 3197

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-11 1552  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-in 3203  df-ss 3210

This theorem is referenced by:  elnn  4698  funimass4  5684  fvelimab  5690  ssimaex  5695  funconstss  5753  rexima  5878  ralima  5879  1st2nd  6327  f1o2ndf1  6374  tfri1dALT  6497  eldju1st  7238  axsuploc  8219  lbinf  9095  dfinfre  9103  lbzbi  9811  elfzom1elp1fzo  10408  ssfzo12  10430  seq3split  10710  seqsplitg  10711  shftlem  11327  uzwodc  12558  subgintm  13735  subrngintm  14176  subrgintm  14207  tgcl  14738  neipsm  14828  txbasval  14941  elmopn2  15123  metrest  15180  cncfmet  15266  negcncf  15279  ply1term  15417  plyconst  15419  reeff1olem  15445  usgruspgrben  15984