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Theorem sseq2i 3090
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 3087 . 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 104    = wceq 1314    C_ wss 3037
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-11 1467  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-in 3043  df-ss 3050
This theorem is referenced by:  sseqtri  3097  syl6sseq  3111  abss  3132  ssrab  3141  ssintrab  3760  iunpwss  3870  iotass  5063  dffun2  5091  ssimaex  5436  isstructim  11816  isstructr  11817  bj-ssom  12826  ss1oel2o  12881
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