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Theorem eqimss2i 3233
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 3197 . 2  |-  B  C_  B
2 eqimssi.1 . 2  |-  A  =  B
31, 2sseqtr4i 3211 1  |-  B  C_  A
Colors of variables: wff set class
Syntax hints:    = wceq 1623    C_ wss 3152
This theorem is referenced by:  supcvg  12314  ef0lem  12360  restid  13338  cayley  14789  gsumval3  15191  gsumzaddlem  15203  kgencn3  17253  hmeores  17462  opnfbas  17537  tsmsf1o  17827  icchmeo  18439  plyeq0lem  19592  ulmdvlem1  19777  basellem7  20324  basellem9  20326  dchrisumlem3  20640  ivthALT  26258  aomclem4  27154  climsuselem1  27733
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-in 3159  df-ss 3166
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