Theorem ssel2 2940

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 2939	. 2 |- ( A C_ B -> ( C e. A -> C e. B ) )
2	1	imp 115	1 |- ( ( A C_ B /\ C e. A ) -> C e. B )

Syntax hints:   -> wi 4   /\ wa 97   e. wcel 1393   C_ wss 2917

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-in 2924  df-ss 2931

This theorem is referenced by:  elnn  4328  funimass4  5224  fvelimab  5229  ssimaex  5234  funconstss  5285  rexima  5394  ralima  5395  1st2nd  5807  f1o2ndf1  5849  lbzbi  8551  elfzom1elp1fzo  9058  ssfzo12  9080  iseqsplit  9238  shftlem  9417