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Theorem dfss5 3546
Description: Another definition of subclasshood. Similar to df-ss 3334, dfss 3335, and dfss1 3545. (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 3545 . 2  |-  ( A 
C_  B  <->  ( B  i^i  A )  =  A )
2 eqcom 2438 . 2  |-  ( ( B  i^i  A )  =  A  <->  A  =  ( B  i^i  A ) )
31, 2bitri 241 1  |-  ( A 
C_  B  <->  A  =  ( B  i^i  A ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    = wceq 1652    i^i cin 3319    C_ wss 3320
This theorem is referenced by:  ordtri2or3  4679  diarnN  31927
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-in 3327  df-ss 3334
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