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Theorem dfss 3055
Description: Variant of subclass definition df-ss 3054. (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 3054 . 2  |-  ( A 
C_  B  <->  ( A  i^i  B )  =  A )
2 eqcom 2119 . 2  |-  ( ( A  i^i  B )  =  A  <->  A  =  ( A  i^i  B ) )
31, 2bitri 183 1  |-  ( A 
C_  B  <->  A  =  ( A  i^i  B ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 104    = wceq 1316    i^i cin 3040    C_ wss 3041
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-gen 1410  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-cleq 2110  df-ss 3054
This theorem is referenced by:  dfss2  3056  onelini  4322  cnvcnv  4961  funimass1  5170  sbthlemi5  6817  dmaddpi  7101  dmmulpi  7102  tgioo  12642
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