Theorem scottss 43002

Description: Scott's trick produces a subset of the input class. (Contributed by Rohan Ridenour, 11-Aug-2023.)

Assertion

Ref	Expression
scottss	⊢ Scott 𝐴 ⊆ 𝐴

Proof of Theorem scottss

Dummy variables 𝑥 𝑦 are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-scott 42995	. 2 ⊢ Scott 𝐴 = {𝑥 ∈ 𝐴 ∣ ∀𝑦 ∈ 𝐴 (rank‘𝑥) ⊆ (rank‘𝑦)}
2	1	ssrab3 4081	1 ⊢ Scott 𝐴 ⊆ 𝐴

Syntax hints:  ∀wral 3062   ⊆ wss 3949  ‘cfv 6544  rankcrnk 9758  Scott cscott 42994

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704

This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-rab 3434  df-v 3477  df-in 3956  df-ss 3966  df-scott 42995

This theorem is referenced by:  elscottab  43003