Theorem ssel2 3142

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 3141	. 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 2141   C_ wss 3121

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 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-11 1499  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-in 3127  df-ss 3134

This theorem is referenced by:  elnn  4590  funimass4  5547  fvelimab  5552  ssimaex  5557  funconstss  5614  rexima  5734  ralima  5735  1st2nd  6160  f1o2ndf1  6207  tfri1dALT  6330  eldju1st  7048  axsuploc  7992  lbinf  8864  dfinfre  8872  lbzbi  9575  elfzom1elp1fzo  10158  ssfzo12  10180  seq3split  10435  shftlem  10780  uzwodc  11992  tgcl  12858  neipsm  12948  txbasval  13061  elmopn2  13243  metrest  13300  cncfmet  13373  negcncf  13382  reeff1olem  13486