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  5686  fvelimab  5692  ssimaex  5697  funconstss  5755  rexima  5884  ralima  5885  1st2nd  6333  f1o2ndf1  6380  tfri1dALT  6503  eldju1st  7249  axsuploc  8230  lbinf  9106  dfinfre  9114  lbzbi  9823  elfzom1elp1fzo  10420  ssfzo12  10442  seq3split  10722  seqsplitg  10723  shftlem  11343  uzwodc  12574  subgintm  13751  subrngintm  14192  subrgintm  14223  tgcl  14754  neipsm  14844  txbasval  14957  elmopn2  15139  metrest  15196  cncfmet  15282  negcncf  15295  ply1term  15433  plyconst  15435  reeff1olem  15461  usgruspgrben  16000