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Theorem ssel2 3062
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 3061 . 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 1465    C_ wss 3041
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 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-11 1469  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-in 3047  df-ss 3054
This theorem is referenced by:  elnn  4489  funimass4  5440  fvelimab  5445  ssimaex  5450  funconstss  5506  rexima  5624  ralima  5625  1st2nd  6047  f1o2ndf1  6093  tfri1dALT  6216  eldju1st  6924  axsuploc  7805  lbinf  8670  dfinfre  8678  lbzbi  9364  elfzom1elp1fzo  9934  ssfzo12  9956  seq3split  10207  shftlem  10543  tgcl  12144  neipsm  12234  txbasval  12347  elmopn2  12529  metrest  12586  cncfmet  12659  negcncf  12668
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