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Theorem eqimssi 3558
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 3523 . 2  |-  A  C_  A
2 eqimssi.1 . 2  |-  A  =  B
31, 2sseqtri 3536 1  |-  A  C_  B
Colors of variables: wff setvar class
Syntax hints:    = wceq 1379    C_ wss 3476
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-in 3483  df-ss 3490
This theorem is referenced by:  funi  5616  fpr  6067  tz7.48-2  7104  trcl  8155  zorn2lem4  8875  zmin  11174  elfzo1  11835  om2uzf1oi  12027  sumsplit  13539  isumless  13613  frlmip  18573  ust0  20454  rrxprds  21553  ovoliunnul  21650  vitalilem5  21753  logtayl  22766  mayetes3i  26321  eulerpartlemsv2  27934  eulerpartlemsv3  27937  eulerpartlemv  27940  eulerpartlemb  27944  dvasin  29678  dvsid  30836  fourierdlem62  31469  fourierdlem66  31473  0trrel  36786
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