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Theorem eqimssi 3153
Description: Infer subclass relationship from equality. (Contributed by NM, 6-Jan-2007.)
Hypothesis
Ref Expression
eqimssi.1  |-  A  =  B
Assertion
Ref Expression
eqimssi  |-  A  C_  B

Proof of Theorem eqimssi
StepHypRef Expression
1 ssid 3117 . 2  |-  A  C_  A
2 eqimssi.1 . 2  |-  A  =  B
31, 2sseqtri 3131 1  |-  A  C_  B
Colors of variables: wff set class
Syntax hints:    = wceq 1331    C_ wss 3071
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-in 3077  df-ss 3084
This theorem is referenced by:  funi  5155  fpr  5602  elfzo1  9974  sumsplitdc  11208  isumlessdc  11272
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