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Theorem dfss 3158
Description: Variant of subclass definition df-ss 3157. (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 3157 . 2  |-  ( A 
C_  B  <->  ( A  i^i  B )  =  A )
2 eqcom 2191 . 2  |-  ( ( A  i^i  B )  =  A  <->  A  =  ( A  i^i  B ) )
31, 2bitri 184 1  |-  ( A 
C_  B  <->  A  =  ( A  i^i  B ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 105    = wceq 1364    i^i cin 3143    C_ wss 3144
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-cleq 2182  df-ss 3157
This theorem is referenced by:  dfss2  3159  onelini  4448  cnvcnv  5099  funimass1  5312  sbthlemi5  6991  dmaddpi  7355  dmmulpi  7356  tgioo  14523
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