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Theorem eqimss2i 4004
Description: Infer subclass relationship from equality. (Contributed by NM, 7-Jan-2007.)
Hypothesis
Ref Expression
eqimssi.1 𝐴 = 𝐵
Assertion
Ref Expression
eqimss2i 𝐵𝐴

Proof of Theorem eqimss2i
StepHypRef Expression
1 ssid 3967 . 2 𝐵𝐵
2 eqimssi.1 . 2 𝐴 = 𝐵
31, 2sseqtrri 3982 1 𝐵𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  wss 3911
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3446  df-in 3918  df-ss 3928
This theorem is referenced by:  cotr3  14869  supcvg  15746  prodfclim1  15783  ef0lem  15966  1strbas  17105  1strbasOLD  17106  restid  17320  cayley  19201  gsumval3  19689  gsumzaddlem  19703  kgencn3  22925  hmeores  23138  opnfbas  23209  tsmsf1o  23512  ust0  23587  icchmeo  24320  plyeq0lem  25587  ulmdvlem1  25775  basellem7  26452  basellem9  26454  dchrisumlem3  26855  structvtxvallem  28013  struct2griedg  28021  gsumhashmul  31947  cycpmfvlem  32010  cycpmfv3  32013  ivthALT  34853  aomclem4  41427  hashnzfzclim  42690  binomcxplemrat  42718  climsuselem1  43934  gsumfsupp  46202
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