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Theorem sseq2i 3049
Description: An equality inference for the subclass relationship. (Contributed by NM, 30-Aug-1993.)
Hypothesis
Ref Expression
sseq1i.1  |-  A  =  B
Assertion
Ref Expression
sseq2i  |-  ( C 
C_  A  <->  C  C_  B
)

Proof of Theorem sseq2i
StepHypRef Expression
1 sseq1i.1 . 2  |-  A  =  B
2 sseq2 3046 . 2  |-  ( A  =  B  ->  ( C  C_  A  <->  C  C_  B
) )
31, 2ax-mp 7 1  |-  ( C 
C_  A  <->  C  C_  B
)
Colors of variables: wff set class
Syntax hints:    <-> wb 103    = wceq 1289    C_ 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:  sseqtri  3056  syl6sseq  3070  abss  3088  ssrab  3097  ssintrab  3706  iunpwss  3812  iotass  4984  dffun2  5012  ssimaex  5349  bj-ssom  11488  ss1oel2o  11545
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