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Theorem dfss5 3205
Description: Another definition of subclasshood. Similar to df-ss 3012, dfss 3013, and dfss1 3204. (Contributed by David Moews, 1-May-2017.)
Assertion
Ref Expression
dfss5  |-  ( A 
C_  B  <->  A  =  ( B  i^i  A ) )

Proof of Theorem dfss5
StepHypRef Expression
1 dfss1 3204 . 2  |-  ( A 
C_  B  <->  ( B  i^i  A )  =  A )
2 eqcom 2090 . 2  |-  ( ( B  i^i  A )  =  A  <->  A  =  ( B  i^i  A ) )
31, 2bitri 182 1  |-  ( A 
C_  B  <->  A  =  ( B  i^i  A ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 103    = wceq 1289    i^i cin 2998    C_ wss 2999
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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-in 3005  df-ss 3012
This theorem is referenced by: (None)
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