Theorem ssel2 3087

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 3086	. 2 |- ( A C_ B -> ( C e. A -> C e. B ) )
2	1	imp 123	1 |- ( ( A C_ B /\ C e. A ) -> C e. B )

Syntax hints:   -> wi 4   /\ wa 103   e. wcel 1480   C_ wss 3066

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119

This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-in 3072  df-ss 3079

This theorem is referenced by:  elnn  4514  funimass4  5465  fvelimab  5470  ssimaex  5475  funconstss  5531  rexima  5649  ralima  5650  1st2nd  6072  f1o2ndf1  6118  tfri1dALT  6241  eldju1st  6949  axsuploc  7830  lbinf  8699  dfinfre  8707  lbzbi  9401  elfzom1elp1fzo  9972  ssfzo12  9994  seq3split  10245  shftlem  10581  tgcl  12222  neipsm  12312  txbasval  12425  elmopn2  12607  metrest  12664  cncfmet  12737  negcncf  12746