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Theorem eqsstr3i 3031
Description: Substitution of equality into a subclass relationship. (Contributed by NM, 19-Oct-1999.)
Hypotheses
Ref Expression
eqsstr3.1  |-  B  =  A
eqsstr3.2  |-  B  C_  C
Assertion
Ref Expression
eqsstr3i  |-  A  C_  C

Proof of Theorem eqsstr3i
StepHypRef Expression
1 eqsstr3.1 . . 3  |-  B  =  A
21eqcomi 2086 . 2  |-  A  =  B
3 eqsstr3.2 . 2  |-  B  C_  C
42, 3eqsstri 3030 1  |-  A  C_  C
Colors of variables: wff set class
Syntax hints:    = wceq 1285    C_ wss 2974
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-in 2980  df-ss 2987
This theorem is referenced by:  inss2  3194  dmv  4579  resasplitss  5100  ofrfval  5751  fnofval  5752  ofrval  5753  off  5755  ofres  5756  ofco  5760  dftpos4  5912  smores2  5943  bcm1k  9784  bcpasc  9790
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