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Theorem ssel2 3123
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
StepHypRef Expression
1 ssel 3122 . 2  |-  ( A 
C_  B  ->  ( C  e.  A  ->  C  e.  B ) )
21imp 123 1  |-  ( ( A  C_  B  /\  C  e.  A )  ->  C  e.  B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    e. wcel 2128    C_ wss 3102
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 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-11 1486  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139
This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-in 3108  df-ss 3115
This theorem is referenced by:  elnn  4567  funimass4  5521  fvelimab  5526  ssimaex  5531  funconstss  5587  rexima  5707  ralima  5708  1st2nd  6131  f1o2ndf1  6177  tfri1dALT  6300  eldju1st  7017  axsuploc  7952  lbinf  8824  dfinfre  8832  lbzbi  9531  elfzom1elp1fzo  10110  ssfzo12  10132  seq3split  10387  shftlem  10727  tgcl  12534  neipsm  12624  txbasval  12737  elmopn2  12919  metrest  12976  cncfmet  13049  negcncf  13058  reeff1olem  13162
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