Theorem ssel2 3151

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 3150	. 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 2148   C_ wss 3130

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 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-in 3136  df-ss 3143

This theorem is referenced by:  elnn  4606  funimass4  5567  fvelimab  5573  ssimaex  5578  funconstss  5635  rexima  5756  ralima  5757  1st2nd  6182  f1o2ndf1  6229  tfri1dALT  6352  eldju1st  7070  axsuploc  8030  lbinf  8905  dfinfre  8913  lbzbi  9616  elfzom1elp1fzo  10202  ssfzo12  10224  seq3split  10479  shftlem  10825  uzwodc  12038  subgintm  13058  subrgintm  13364  tgcl  13567  neipsm  13657  txbasval  13770  elmopn2  13952  metrest  14009  cncfmet  14082  negcncf  14091  reeff1olem  14195