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Theorem sseqin2 3202
Description: A relationship between subclass and intersection. Similar to Exercise 9 of [TakeutiZaring] p. 18. (Contributed by NM, 17-May-1994.)
Assertion
Ref Expression
sseqin2  |-  ( A 
C_  B  <->  ( B  i^i  A )  =  A )

Proof of Theorem sseqin2
StepHypRef Expression
1 dfss1 3187 1  |-  ( A 
C_  B  <->  ( B  i^i  A )  =  A )
Colors of variables: wff set class
Syntax hints:    <-> wb 103    = wceq 1285    i^i cin 2982    C_ wss 2983
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-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612  df-in 2989  df-ss 2996
This theorem is referenced by:  resabs1  4689  rescnvcnv  4834  frecfnom  6071  nn0supp  8443  uzin  8768  iooval2  9050  fzval2  9144  dfphi2  10787
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