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Theorem eqimss2 3231
Description: Equality implies the subclass relation. (Contributed by NM, 23-Nov-2003.)
Assertion
Ref Expression
eqimss2  |-  ( B  =  A  ->  A  C_  B )

Proof of Theorem eqimss2
StepHypRef Expression
1 eqimss 3230 . 2  |-  ( A  =  B  ->  A  C_  B )
21eqcoms 2286 1  |-  ( B  =  A  ->  A  C_  B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1623    C_ wss 3152
This theorem is referenced by:  disjeq2  3997  disjeq1  4000  poeq2  4318  freq2  4364  seeq1  4365  seeq2  4366  suc11  4496  dmcoeq  4947  xp11  5111  funeq  5274  fconst3  5735  tposeq  6236  sorpssuni  6286  sorpssint  6287  oaass  6559  odi  6577  oen0  6584  inficl  7178  cantnfp1lem1  7380  cantnfp1lem3  7382  cantnflem1d  7390  cantnflem1  7391  fodomfi2  7687  zorng  8131  rlimclim  12020  imasaddfnlem  13430  imasvscafn  13439  gasubg  14756  pgpssslw  14925  dprddisj2  15274  dprd2da  15277  ply1coe  16368  frgpcyg  16527  topgele  16672  topontopn  16680  toponmre  16830  conima  17151  ptbasfi  17276  txdis  17326  neifil  17575  elfm3  17645  rnelfmlem  17647  alexsubALTlem3  17743  alexsubALTlem4  17744  lmclimf  18729  uniiccdif  18933  dv11cn  19348  evlslem6  19397  plypf1  19594  subgores  20971  hstoh  22812  dmdi2  22884  rrvdmss  23652  dfps2  25289  basexre  25522  refssfne  26294  islocfin  26296  neibastop3  26311  topmeet  26313  topjoin  26314  fnemeet2  26316  fnejoin1  26317  heiborlem3  26537  uvcresum  27242  ssrecnpr  27537  lsatelbN  29196  lkrscss  29288  lshpset2N  29309  mapdrvallem2  31835  hdmaprnlem3eN  32051  hdmaplkr  32106
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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