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Theorem sseq1i 3093
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  |-  ( A 
C_  C  <->  B  C_  C
)

Proof of Theorem sseq1i
StepHypRef Expression
1 sseq1i.1 . 2  |-  A  =  B
2 sseq1 3090 . 2  |-  ( A  =  B  ->  ( A  C_  C  <->  B  C_  C
) )
31, 2ax-mp 5 1  |-  ( A 
C_  C  <->  B  C_  C
)
Colors of variables: wff set class
Syntax hints:    <-> wb 104    = wceq 1316    C_ wss 3041
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 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-11 1469  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-in 3047  df-ss 3054
This theorem is referenced by:  eqsstri  3099  eqsstrid  3113  ssab  3137  rabss  3144  uniiunlem  3155  prss  3646  prssg  3647  tpss  3655  iunss  3824  pwtr  4111  ordsucss  4390  elnn  4489  cores2  5021  dffun2  5103  funimaexglem  5176  idref  5626  ordgt0ge1  6300  prarloclemn  7275  bdeqsuc  13006  bj-omssind  13060
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