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Theorem eqimssi 3123
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 3087 . 2  |-  A  C_  A
2 eqimssi.1 . 2  |-  A  =  B
31, 2sseqtri 3101 1  |-  A  C_  B
Colors of variables: wff set class
Syntax hints:    = wceq 1316    C_ wss 3041
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 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-11 1469  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-in 3047  df-ss 3054
This theorem is referenced by:  funi  5125  fpr  5570  elfzo1  9935  sumsplitdc  11169  isumlessdc  11233
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