Theorem ssel2 3097

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 3096	. 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 1481   C_ wss 3076

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 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-11 1485  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122

This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-in 3082  df-ss 3089

This theorem is referenced by:  elnn  4527  funimass4  5480  fvelimab  5485  ssimaex  5490  funconstss  5546  rexima  5664  ralima  5665  1st2nd  6087  f1o2ndf1  6133  tfri1dALT  6256  eldju1st  6964  axsuploc  7861  lbinf  8730  dfinfre  8738  lbzbi  9435  elfzom1elp1fzo  10010  ssfzo12  10032  seq3split  10283  shftlem  10620  tgcl  12272  neipsm  12362  txbasval  12475  elmopn2  12657  metrest  12714  cncfmet  12787  negcncf  12796  reeff1olem  12900