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Theorem dfss5 3189
Description: Another definition of subclasshood. Similar to df-ss 2997, dfss 2998, and dfss1 3188. (Contributed by David Moews, 1-May-2017.)
Assertion
Ref Expression
dfss5 (𝐴𝐵𝐴 = (𝐵𝐴))

Proof of Theorem dfss5
StepHypRef Expression
1 dfss1 3188 . 2 (𝐴𝐵 ↔ (𝐵𝐴) = 𝐴)
2 eqcom 2085 . 2 ((𝐵𝐴) = 𝐴𝐴 = (𝐵𝐴))
31, 2bitri 182 1 (𝐴𝐵𝐴 = (𝐵𝐴))
Colors of variables: wff set class
Syntax hints:  wb 103   = wceq 1285  cin 2983  wss 2984
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 2614  df-in 2990  df-ss 2997
This theorem is referenced by: (None)
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