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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 (𝐴𝐵𝐴 = (𝐴𝐵))

Proof of Theorem dfss
StepHypRef Expression
1 df-ss 3010 . 2 (𝐴𝐵 ↔ (𝐴𝐵) = 𝐴)
2 eqcom 2090 . 2 ((𝐴𝐵) = 𝐴𝐴 = (𝐴𝐵))
31, 2bitri 182 1 (𝐴𝐵𝐴 = (𝐴𝐵))
Colors of variables: wff set class
Syntax hints:  wb 103   = wceq 1289  cin 2996  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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