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Theorem sseqtrri 3132
 Description: Substitution of equality into a subclass relationship. (Contributed by NM, 4-Apr-1995.)
Hypotheses
Ref Expression
sseqtrri.1 𝐴𝐵
sseqtrri.2 𝐶 = 𝐵
Assertion
Ref Expression
sseqtrri 𝐴𝐶

Proof of Theorem sseqtrri
StepHypRef Expression
1 sseqtrri.1 . 2 𝐴𝐵
2 sseqtrri.2 . . 3 𝐶 = 𝐵
32eqcomi 2143 . 2 𝐵 = 𝐶
41, 3sseqtri 3131 1 𝐴𝐶
 Colors of variables: wff set class Syntax hints:   = wceq 1331   ⊆ wss 3071 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 2121 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-in 3077  df-ss 3084 This theorem is referenced by:  eqimss2i  3154  difdif2ss  3333  snsspr1  3668  snsspr2  3669  snsstp1  3670  snsstp2  3671  snsstp3  3672  prsstp12  3673  prsstp13  3674  prsstp23  3675  iunxdif2  3861  pwpwssunieq  3901  sssucid  4337  opabssxp  4613  dmresi  4874  cnvimass  4902  ssrnres  4981  cnvcnv  4991  cnvssrndm  5060  dmmpossx  6097  tfrcllemssrecs  6249  sucinc  6341  mapex  6548  exmidpw  6802  casefun  6970  djufun  6989  ressxr  7809  ltrelxr  7825  nnssnn0  8980  un0addcl  9010  un0mulcl  9011  nn0ssxnn0  9043  fzssnn  9848  fzossnn0  9952  isumclim3  11192  isprm3  11799  phimullem  11901  tgvalex  12219  cnrest2  12405  qtopbasss  12690  tgqioo  12716
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