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Theorem eqimss2i 3347
Description: Infer subclass relationship from equality. (Contributed by NM, 7-Jan-2007.)
Hypothesis
Ref Expression
eqimssi.1  |-  A  =  B
Assertion
Ref Expression
eqimss2i  |-  B  C_  A

Proof of Theorem eqimss2i
StepHypRef Expression
1 ssid 3311 . 2  |-  B  C_  B
2 eqimssi.1 . 2  |-  A  =  B
31, 2sseqtr4i 3325 1  |-  B  C_  A
Colors of variables: wff set class
Syntax hints:    = wceq 1649    C_ wss 3264
This theorem is referenced by:  supcvg  12563  ef0lem  12609  restid  13589  cayley  15040  gsumval3  15442  gsumzaddlem  15454  kgencn3  17512  hmeores  17725  opnfbas  17796  tsmsf1o  18096  ust0  18171  icchmeo  18838  plyeq0lem  19997  ulmdvlem1  20184  basellem7  20737  basellem9  20739  dchrisumlem3  21053  prodfclim1  25001  ivthALT  26030  aomclem4  26824  climsuselem1  27402
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2369
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2375  df-cleq 2381  df-clel 2384  df-in 3271  df-ss 3278
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