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Theorem sseq1i 2963
Description: An equality inference for the subclass relationship. (Contributed by NM, 18-Aug-1993.)
Hypothesis
Ref Expression
sseq1i.1 A = B
Assertion
Ref Expression
sseq1i (A𝐶B𝐶)

Proof of Theorem sseq1i
StepHypRef Expression
1 sseq1i.1 . 2 A = B
2 sseq1 2960 . 2 (A = B → (A𝐶B𝐶))
31, 2ax-mp 7 1 (A𝐶B𝐶)
Colors of variables: wff set class
Syntax hints:  wb 98   = wceq 1242  wss 2911
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-in 2918  df-ss 2925
This theorem is referenced by:  eqsstri  2969  syl5eqss  2983  ssab  3004  rabss  3011  uniiunlem  3022  prss  3511  prssg  3512  tpss  3520  iunss  3689  pwtr  3946  ordsucss  4196  elnn  4271  cores2  4776  dffun2  4855  funimaexglem  4925  idref  5339  ordgt0ge1  5957  prarloclemn  6481  bdeqsuc  9316  bj-omssind  9369
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