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Theorem dfss 3053
Description: Variant of subclass definition df-ss 3052. (Contributed by NM, 3-Sep-2004.)
Assertion
Ref Expression
dfss (𝐴𝐵𝐴 = (𝐴𝐵))

Proof of Theorem dfss
StepHypRef Expression
1 df-ss 3052 . 2 (𝐴𝐵 ↔ (𝐴𝐵) = 𝐴)
2 eqcom 2117 . 2 ((𝐴𝐵) = 𝐴𝐴 = (𝐴𝐵))
31, 2bitri 183 1 (𝐴𝐵𝐴 = (𝐴𝐵))
Colors of variables: wff set class
Syntax hints:  wb 104   = wceq 1314  cin 3038  wss 3039
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 1406  ax-gen 1408  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-cleq 2108  df-ss 3052
This theorem is referenced by:  dfss2  3054  onelini  4320  cnvcnv  4959  funimass1  5168  sbthlemi5  6815  dmaddpi  7097  dmmulpi  7098  tgioo  12621
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