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Theorem dfss5 3374
Description: Another definition of subclasshood. Similar to df-ss 3166, dfss 3167, and dfss1 3373. (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 3373 . 2  |-  ( A 
C_  B  <->  ( B  i^i  A )  =  A )
2 eqcom 2285 . 2  |-  ( ( B  i^i  A )  =  A  <->  A  =  ( B  i^i  A ) )
31, 2bitri 240 1  |-  ( A 
C_  B  <->  A  =  ( B  i^i  A ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    = wceq 1623    i^i cin 3151    C_ wss 3152
This theorem is referenced by:  ordtri2or3  4490
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-in 3159  df-ss 3166
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