Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  eqimssi Unicode version

Theorem eqimssi 3245
 Description: Infer subclass relationship from equality. (Contributed by NM, 6-Jan-2007.)
Hypothesis
Ref Expression
eqimssi.1
Assertion
Ref Expression
eqimssi

Proof of Theorem eqimssi
StepHypRef Expression
1 ssid 3210 . 2
2 eqimssi.1 . 2
31, 2sseqtri 3223 1
 Colors of variables: wff set class Syntax hints:   wceq 1632   wss 3165 This theorem is referenced by:  funi  5300  fpr  5720  tz7.48-2  6470  trcl  7426  zorn2lem4  8142  zmin  10328  om2uzf1oi  11032  sumsplit  12247  isumless  12320  ovoliunnul  18882  vitalilem5  18983  logtayl  20023  mayetes3i  22325  elfzo1  23294  sqpsym  25176  empos  25345  dispos  25390  1alg  25825  0alg  25859  dvsid  27651 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-in 3172  df-ss 3179
 Copyright terms: Public domain W3C validator