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Theorem eqsstr3i 3615
Description: Substitution of equality into a subclass relationship. (Contributed by NM, 19-Oct-1999.)
Hypotheses
Ref Expression
eqsstr3.1 𝐵 = 𝐴
eqsstr3.2 𝐵𝐶
Assertion
Ref Expression
eqsstr3i 𝐴𝐶

Proof of Theorem eqsstr3i
StepHypRef Expression
1 eqsstr3.1 . . 3 𝐵 = 𝐴
21eqcomi 2630 . 2 𝐴 = 𝐵
3 eqsstr3.2 . 2 𝐵𝐶
42, 3eqsstri 3614 1 𝐴𝐶
Colors of variables: wff setvar class
Syntax hints:   = wceq 1480  wss 3555
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-in 3562  df-ss 3569
This theorem is referenced by:  inss2  3812  dmv  5301  ofrfval  6858  ofval  6859  ofrval  6860  off  6865  ofres  6866  ofco  6870  dftpos4  7316  smores2  7396  onwf  8637  r0weon  8779  cda1dif  8942  unctb  8971  infmap2  8984  itunitc  9187  axcclem  9223  dfnn3  10978  bcm1k  13042  bcpasc  13048  cotr2  13650  ressbasss  15853  strlemor1OLD  15890  prdsle  16043  prdsless  16044  dprd2da  18362  opsrle  19394  indiscld  20805  leordtval2  20926  fiuncmp  21117  prdstopn  21341  ustneism  21937  itg1addlem4  23372  itg1addlem5  23373  tdeglem4  23724  aannenlem3  23989  efifo  24197  advlogexp  24301  konigsbergssiedgw  26977  pjoml4i  28292  5oai  28366  3oai  28373  bdopssadj  28786  xrge00  29468  xrge0mulc1cn  29766  esumdivc  29923  ballotlemodife  30337  subfacp1lem5  30871  filnetlem3  32014  filnetlem4  32015  mblfinlem4  33078  itg2gt0cn  33094  psubspset  34507  psubclsetN  34699  relexpaddss  37488  corcltrcl  37509  relopabVD  38617  cncfiooicc  39408  stoweidlem34  39555  amgmwlem  41848
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