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Theorem ssel2 3142
Description: Membership relationships follow from a subclass relationship. (Contributed by NM, 7-Jun-2004.)
Assertion
Ref Expression
ssel2 ((𝐴𝐵𝐶𝐴) → 𝐶𝐵)

Proof of Theorem ssel2
StepHypRef Expression
1 ssel 3141 . 2 (𝐴𝐵 → (𝐶𝐴𝐶𝐵))
21imp 123 1 ((𝐴𝐵𝐶𝐴) → 𝐶𝐵)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wcel 2141  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  4588  funimass4  5545  fvelimab  5550  ssimaex  5555  funconstss  5611  rexima  5731  ralima  5732  1st2nd  6157  f1o2ndf1  6204  tfri1dALT  6327  eldju1st  7044  axsuploc  7979  lbinf  8851  dfinfre  8859  lbzbi  9562  elfzom1elp1fzo  10145  ssfzo12  10167  seq3split  10422  shftlem  10767  uzwodc  11979  tgcl  12779  neipsm  12869  txbasval  12982  elmopn2  13164  metrest  13221  cncfmet  13294  negcncf  13303  reeff1olem  13407
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