Theorem ssel2 3222

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 3221	. 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 2202   C_ wss 3200

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 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-11 1554  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-in 3206  df-ss 3213

This theorem is referenced by:  elnn  4704  funimass4  5696  fvelimab  5702  ssimaex  5707  funconstss  5765  rexima  5895  ralima  5896  1st2nd  6344  f1o2ndf1  6393  tfri1dALT  6517  eldju1st  7270  axsuploc  8252  lbinf  9128  dfinfre  9136  lbzbi  9850  elfzom1elp1fzo  10448  ssfzo12  10470  seq3split  10751  seqsplitg  10752  shftlem  11394  uzwodc  12626  subgintm  13803  subrngintm  14245  subrgintm  14276  tgcl  14807  neipsm  14897  txbasval  15010  elmopn2  15192  metrest  15249  cncfmet  15335  negcncf  15348  ply1term  15486  plyconst  15488  reeff1olem  15514  usgruspgrben  16056