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Theorem sseqtrri 3127
Description: Substitution of equality into a subclass relationship. (Contributed by NM, 4-Apr-1995.)
Hypotheses
Ref Expression
sseqtrri.1  |-  A  C_  B
sseqtrri.2  |-  C  =  B
Assertion
Ref Expression
sseqtrri  |-  A  C_  C

Proof of Theorem sseqtrri
StepHypRef Expression
1 sseqtrri.1 . 2  |-  A  C_  B
2 sseqtrri.2 . . 3  |-  C  =  B
32eqcomi 2141 . 2  |-  B  =  C
41, 3sseqtri 3126 1  |-  A  C_  C
Colors of variables: wff set class
Syntax hints:    = wceq 1331    C_ wss 3066
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119
This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-in 3072  df-ss 3079
This theorem is referenced by:  eqimss2i  3149  difdif2ss  3328  snsspr1  3663  snsspr2  3664  snsstp1  3665  snsstp2  3666  snsstp3  3667  prsstp12  3668  prsstp13  3669  prsstp23  3670  iunxdif2  3856  pwpwssunieq  3896  sssucid  4332  opabssxp  4608  dmresi  4869  cnvimass  4897  ssrnres  4976  cnvcnv  4986  cnvssrndm  5055  dmmpossx  6090  tfrcllemssrecs  6242  sucinc  6334  mapex  6541  exmidpw  6795  casefun  6963  djufun  6982  ressxr  7802  ltrelxr  7818  nnssnn0  8973  un0addcl  9003  un0mulcl  9004  nn0ssxnn0  9036  fzssnn  9841  fzossnn0  9945  isumclim3  11185  isprm3  11788  phimullem  11890  tgvalex  12208  cnrest2  12394  qtopbasss  12679  tgqioo  12705
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