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Theorem dfss5 3136
Description: Another definition of subclasshood. Similar to df-ss 2925, dfss 2926, and dfss1 3135. (Contributed by David Moews, 1-May-2017.)
Assertion
Ref Expression
dfss5 (ABA = (BA))

Proof of Theorem dfss5
StepHypRef Expression
1 dfss1 3135 . 2 (AB ↔ (BA) = A)
2 eqcom 2039 . 2 ((BA) = AA = (BA))
31, 2bitri 173 1 (ABA = (BA))
Colors of variables: wff set class
Syntax hints:  wb 98   = wceq 1242  cin 2910  wss 2911
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-in 2918  df-ss 2925
This theorem is referenced by: (None)
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