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Theorem sseqin2 3354
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 (𝐴𝐵 ↔ (𝐵𝐴) = 𝐴)

Proof of Theorem sseqin2
StepHypRef Expression
1 dfss1 3339 1 (𝐴𝐵 ↔ (𝐵𝐴) = 𝐴)
Colors of variables: wff set class
Syntax hints:  wb 105   = wceq 1353  cin 3128  wss 3129
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-in 3135  df-ss 3142
This theorem is referenced by:  dfss4st  3368  resabs1  4932  rescnvcnv  5087  frecfnom  6396  fiintim  6922  nn0supp  9217  uzin  9549  iooval2  9902  fzval2  9998  suprzubdc  11936  dfphi2  12203  ressabsg  12517  resttopon  13338  restabs  13342  restopnb  13348  txcnmpt  13440
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