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Theorem dfss 2959
Description: Variant of subclass definition df-ss 2958. (Contributed by NM, 3-Sep-2004.)
Assertion
Ref Expression
dfss (𝐴𝐵𝐴 = (𝐴𝐵))

Proof of Theorem dfss
StepHypRef Expression
1 df-ss 2958 . 2 (𝐴𝐵 ↔ (𝐴𝐵) = 𝐴)
2 eqcom 2058 . 2 ((𝐴𝐵) = 𝐴𝐴 = (𝐴𝐵))
31, 2bitri 177 1 (𝐴𝐵𝐴 = (𝐴𝐵))
Colors of variables: wff set class
Syntax hints:  wb 102   = wceq 1259  cin 2943  wss 2944
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-cleq 2049  df-ss 2958
This theorem is referenced by:  dfss2  2961  onelini  4194  cnvcnv  4800  funimass1  5003  dmaddpi  6480  dmmulpi  6481
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