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Theorem sseq1i 3048
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 3045 . 2 (𝐴 = 𝐵 → (𝐴𝐶𝐵𝐶))
31, 2ax-mp 7 1 (𝐴𝐶𝐵𝐶)
Colors of variables: wff set class
Syntax hints:  wb 103   = wceq 1289  wss 2997
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-11 1442  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-in 3003  df-ss 3010
This theorem is referenced by:  eqsstri  3054  syl5eqss  3068  ssab  3089  rabss  3096  uniiunlem  3107  prss  3588  prssg  3589  tpss  3597  iunss  3766  pwtr  4037  ordsucss  4311  elnn  4410  cores2  4930  dffun2  5012  funimaexglem  5083  idref  5518  ordgt0ge1  6181  prarloclemn  7037  bdeqsuc  11429  bj-omssind  11487
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