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Theorem dfss 2960
Description: Variant of subclass definition df-ss 2959. (Contributed by NM, 3-Sep-2004.)
Assertion
Ref Expression
dfss  |-  ( A 
C_  B  <->  A  =  ( A  i^i  B ) )

Proof of Theorem dfss
StepHypRef Expression
1 df-ss 2959 . 2  |-  ( A 
C_  B  <->  ( A  i^i  B )  =  A )
2 eqcom 2058 . 2  |-  ( ( A  i^i  B )  =  A  <->  A  =  ( A  i^i  B ) )
31, 2bitri 177 1  |-  ( A 
C_  B  <->  A  =  ( A  i^i  B ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 102    = wceq 1259    i^i cin 2944    C_ wss 2945
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-cleq 2049  df-ss 2959
This theorem is referenced by:  dfss2  2962  onelini  4195  cnvcnv  4801  funimass1  5004  dmaddpi  6481  dmmulpi  6482
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