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Theorem eqimssi 3232
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 3197 . 2  |-  A  C_  A
2 eqimssi.1 . 2  |-  A  =  B
31, 2sseqtri 3210 1  |-  A  C_  B
Colors of variables: wff set class
Syntax hints:    = wceq 1623    C_ wss 3152
This theorem is referenced by:  funi  5284  fpr  5704  tz7.48-2  6454  trcl  7410  zorn2lem4  8126  zmin  10312  om2uzf1oi  11016  sumsplit  12231  isumless  12304  ovoliunnul  18866  vitalilem5  18967  logtayl  20007  mayetes3i  22309  elfzo1  23279  sqpsym  25073  empos  25242  dispos  25287  1alg  25722  0alg  25756  dvsid  27548
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-in 3159  df-ss 3166
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