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Theorem dfss5 3281
Description: Another definition of subclasshood. Similar to df-ss 3084, dfss 3085, and dfss1 3280. (Contributed by David Moews, 1-May-2017.)
Assertion
Ref Expression
dfss5 (𝐴𝐵𝐴 = (𝐵𝐴))

Proof of Theorem dfss5
StepHypRef Expression
1 dfss1 3280 . 2 (𝐴𝐵 ↔ (𝐵𝐴) = 𝐴)
2 eqcom 2141 . 2 ((𝐵𝐴) = 𝐴𝐴 = (𝐵𝐴))
31, 2bitri 183 1 (𝐴𝐵𝐴 = (𝐵𝐴))
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: (None)
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