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Theorem eqimss2i 3246
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 3210 . 2  |-  B  C_  B
2 eqimssi.1 . 2  |-  A  =  B
31, 2sseqtr4i 3224 1  |-  B  C_  A
Colors of variables: wff set class
Syntax hints:    = wceq 1632    C_ wss 3165
This theorem is referenced by:  supcvg  12330  ef0lem  12376  restid  13354  cayley  14805  gsumval3  15207  gsumzaddlem  15219  kgencn3  17269  hmeores  17478  opnfbas  17553  tsmsf1o  17843  icchmeo  18455  plyeq0lem  19608  ulmdvlem1  19793  basellem7  20340  basellem9  20342  dchrisumlem3  20656  prodfclim1  24167  ivthALT  26361  aomclem4  27257  climsuselem1  27836
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-in 3172  df-ss 3179
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