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Theorem eqimssi 3402
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 3367 . 2  |-  A  C_  A
2 eqimssi.1 . 2  |-  A  =  B
31, 2sseqtri 3380 1  |-  A  C_  B
Colors of variables: wff set class
Syntax hints:    = wceq 1652    C_ wss 3320
This theorem is referenced by:  funi  5483  fpr  5914  tz7.48-2  6699  trcl  7664  zorn2lem4  8379  zmin  10570  elfzo1  11173  om2uzf1oi  11293  sumsplit  12552  isumless  12625  ust0  18249  ovoliunnul  19403  vitalilem5  19504  logtayl  20551  mayetes3i  23232  dvsid  27525
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-in 3327  df-ss 3334
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