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Theorem scottss 44267
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 44260 . 2 Scott 𝐴 = {𝑥𝐴 ∣ ∀𝑦𝐴 (rank‘𝑥) ⊆ (rank‘𝑦)}
21ssrab3 4081 1 Scott 𝐴𝐴
Colors of variables: wff setvar class
Syntax hints:  wral 3060  wss 3950  cfv 6560  rankcrnk 9804  Scott cscott 44259
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-rab 3436  df-ss 3967  df-scott 44260
This theorem is referenced by:  elscottab  44268
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