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Theorem dfss 2998
Description: Variant of subclass definition df-ss 2997. (Contributed by NM, 3-Sep-2004.)
Assertion
Ref Expression
dfss (𝐴𝐵𝐴 = (𝐴𝐵))

Proof of Theorem dfss
StepHypRef Expression
1 df-ss 2997 . 2 (𝐴𝐵 ↔ (𝐴𝐵) = 𝐴)
2 eqcom 2085 . 2 ((𝐴𝐵) = 𝐴𝐴 = (𝐴𝐵))
31, 2bitri 182 1 (𝐴𝐵𝐴 = (𝐴𝐵))
Colors of variables: wff set class
Syntax hints:  wb 103   = wceq 1285  cin 2983  wss 2984
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 1377  ax-gen 1379  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-cleq 2076  df-ss 2997
This theorem is referenced by:  dfss2  2999  onelini  4221  cnvcnv  4837  funimass1  5044  dmaddpi  6787  dmmulpi  6788
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