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Theorem dfss5 3387
Description: Another definition of subclasshood. Similar to df-ss 3179, dfss 3180, and dfss1 3386. (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 3386 . 2  |-  ( A 
C_  B  <->  ( B  i^i  A )  =  A )
2 eqcom 2298 . 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 1632    i^i cin 3164    C_ wss 3165
This theorem is referenced by:  ordtri2or3  4506
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-in 3172  df-ss 3179
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