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Theorem eqimss2i 3212
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 3175 . 2  |-  B  C_  B
2 eqimssi.1 . 2  |-  A  =  B
31, 2sseqtrri 3190 1  |-  B  C_  A
Colors of variables: wff set class
Syntax hints:    = wceq 1353    C_ wss 3129
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-in 3135  df-ss 3142
This theorem is referenced by:  cocnvres  5149  cocnvss  5150  fsum3  11379  prodfclim1  11536  ef0lem  11652  restid  12647  hmeores  13482
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