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Theorem scottss 44239
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 44232 . 2 Scott 𝐴 = {𝑥𝐴 ∣ ∀𝑦𝐴 (rank‘𝑥) ⊆ (rank‘𝑦)}
21ssrab3 4092 1 Scott 𝐴𝐴
Colors of variables: wff setvar class
Syntax hints:  wral 3059  wss 3963  cfv 6563  rankcrnk 9801  Scott cscott 44231
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-rab 3434  df-ss 3980  df-scott 44232
This theorem is referenced by:  elscottab  44240
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