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Theorem dfss5 3642
Description: Another definition of subclasshood. Similar to df-ss 3425, dfss 3426, and dfss1 3641. (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 3641 . 2  |-  ( A 
C_  B  <->  ( B  i^i  A )  =  A )
2 eqcom 2409 . 2  |-  ( ( B  i^i  A )  =  A  <->  A  =  ( B  i^i  A ) )
31, 2bitri 249 1  |-  ( A 
C_  B  <->  A  =  ( B  i^i  A ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    = wceq 1403    i^i cin 3410    C_ wss 3411
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1637  ax-4 1650  ax-5 1723  ax-6 1769  ax-7 1812  ax-10 1859  ax-11 1864  ax-12 1876  ax-13 2024  ax-ext 2378
This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1406  df-ex 1632  df-nf 1636  df-sb 1762  df-clab 2386  df-cleq 2392  df-clel 2395  df-nfc 2550  df-v 3058  df-in 3418  df-ss 3425
This theorem is referenced by:  ordtri2or3  4916  difuncomp  27729  diarnN  34113
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