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Theorem scottss 42987
Description: Scott's trick produces a subset of the input class. (Contributed by Rohan Ridenour, 11-Aug-2023.)
Assertion
Ref Expression
scottss Scott 𝐴𝐴

Proof of Theorem scottss
Dummy variables 𝑥 𝑦 are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-scott 42980 . 2 Scott 𝐴 = {𝑥𝐴 ∣ ∀𝑦𝐴 (rank‘𝑥) ⊆ (rank‘𝑦)}
21ssrab3 4079 1 Scott 𝐴𝐴
Colors of variables: wff setvar class
Syntax hints:  wral 3061  wss 3947  cfv 6540  rankcrnk 9754  Scott cscott 42979
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-rab 3433  df-v 3476  df-in 3954  df-ss 3964  df-scott 42980
This theorem is referenced by:  elscottab  42988
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