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Theorem sseqin2 3295
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 3280 1 (𝐴𝐵 ↔ (𝐵𝐴) = 𝐴)
Colors of variables: wff set class
Syntax hints:  wb 104   = wceq 1331  cin 3070  wss 3071
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-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-in 3077  df-ss 3084
This theorem is referenced by:  dfss4st  3309  resabs1  4848  rescnvcnv  5001  frecfnom  6298  fiintim  6817  nn0supp  9041  uzin  9370  iooval2  9710  fzval2  9805  dfphi2  11907  resttopon  12354  restabs  12358  restopnb  12364  txcnmpt  12456
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