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Theorem dfss 3011
Description: Variant of subclass definition df-ss 3010. (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 3010 . 2  |-  ( A 
C_  B  <->  ( A  i^i  B )  =  A )
2 eqcom 2090 . 2  |-  ( ( A  i^i  B )  =  A  <->  A  =  ( A  i^i  B ) )
31, 2bitri 182 1  |-  ( A 
C_  B  <->  A  =  ( A  i^i  B ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 103    = wceq 1289    i^i cin 2996    C_ wss 2997
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-cleq 2081  df-ss 3010
This theorem is referenced by:  dfss2  3012  onelini  4248  cnvcnv  4870  funimass1  5077  sbthlemi5  6649  dmaddpi  6863  dmmulpi  6864
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