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Theorem scottss 40889
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 40882 . 2 Scott 𝐴 = {𝑥𝐴 ∣ ∀𝑦𝐴 (rank‘𝑥) ⊆ (rank‘𝑦)}
21ssrab3 4032 1 Scott 𝐴𝐴
Colors of variables: wff setvar class
Syntax hints:  wral 3130  wss 3908  cfv 6334  rankcrnk 9180  Scott cscott 40881
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 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2178  ax-ext 2794
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2801  df-cleq 2815  df-clel 2894  df-nfc 2962  df-rab 3139  df-v 3471  df-in 3915  df-ss 3925  df-scott 40882
This theorem is referenced by:  elscottab  40890
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