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Theorem sseq2i 3947
Description: An equality inference for the subclass relationship. (Contributed by NM, 30-Aug-1993.)
Hypothesis
Ref Expression
sseq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
sseq2i (𝐶𝐴𝐶𝐵)

Proof of Theorem sseq2i
StepHypRef Expression
1 sseq1i.1 . 2 𝐴 = 𝐵
2 sseq2 3944 . 2 (𝐴 = 𝐵 → (𝐶𝐴𝐶𝐵))
31, 2ax-mp 5 1 (𝐶𝐴𝐶𝐵)
Colors of variables: wff setvar class
Syntax hints:  wb 209   = wceq 1538  wss 3884
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2114  ax-9 2122  ax-ext 2773
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2070  df-clab 2780  df-cleq 2794  df-clel 2873  df-v 3446  df-in 3891  df-ss 3901
This theorem is referenced by:  sseqtri  3954  sseqtrdi  3968  abss  3991  ssrab  4003  ssindif0  4374  difcom  4395  ssunsn2  4723  ssunpr  4728  sspr  4729  sstp  4730  ssintrab  4864  iunpwss  4995  propssopi  5366  dffun2  6338  ssimaex  6727  elpwun  7475  frfi  8751  alephislim  9498  cardaleph  9504  fin1a2lem12  9826  zornn0g  9920  ssxr  10703  nnwo  12305  isstruct  16492  issubm  17964  grpissubg  18295  islinds  20502  basdif0  21562  tgdif0  21601  cmpsublem  22008  cmpsub  22009  hauscmplem  22015  2ndcctbss  22064  fbncp  22448  cnextfval  22671  eltsms  22742  reconn  23437  cmssmscld  23958  axcontlem3  26764  axcontlem4  26765  umgredg  26935  nbuhgr  27137  uhgrvd00  27328  vtxdginducedm1  27337  chsscon1i  29249  hatomistici  30149  chirredlem4  30180  atabs2i  30189  mdsymlem1  30190  mdsymlem3  30192  mdsymlem6  30195  mdsymlem8  30197  dmdbr5ati  30209  iundifdif  30330  nocvxminlem  33361  nocvxmin  33362  poimir  35089  ismblfin  35097  cossssid2  35867  ntrk0kbimka  40739  ntrclsk3  40770  ntrneicls11  40790  abssf  41745  ssrabf  41747  stoweidlem57  42696  ovnsubadd  43208  ovnovollem3  43294  issubmgm  44406  linccl  44820  lincdifsn  44830
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