Theorem ssel2 3243

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 3242	. 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 2209   C_ wss 3220

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 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-11 1559  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This theorem depends on definitions:  df-bi 117  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-in 3226  df-ss 3233

This theorem is referenced by:  elnn  4748  funimass4  5747  fvelimab  5753  ssimaex  5758  funconstss  5818  rexima  5950  ralima  5951  1st2nd  6405  f1o2ndf1  6454  tfri1dALT  6612  eldju1st  7401  axsuploc  8388  lbinf  9268  dfinfre  9276  lbzbi  9995  elfzom1elp1fzo  10598  ssfzo12  10620  seq3split  10903  seqsplitg  10904  shftlem  11559  uzwodc  12792  subgintm  13978  subrngintm  14493  subrgintm  14524  tgcl  15088  neipsm  15178  txbasval  15291  elmopn2  15473  metrest  15530  cncfmet  15616  negcncf  15629  ply1term  15767  plyconst  15769  reeff1olem  15795  usgruspgrben  16341