Theorem scottss 41861

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 41854	. 2 ⊢ Scott 𝐴 = {𝑥 ∈ 𝐴 ∣ ∀𝑦 ∈ 𝐴 (rank‘𝑥) ⊆ (rank‘𝑦)}
2	1	ssrab3 4015	1 ⊢ Scott 𝐴 ⊆ 𝐴

Syntax hints:  ∀wral 3064   ⊆ wss 3887  ‘cfv 6433  rankcrnk 9521  Scott cscott 41853

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1542  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-rab 3073  df-v 3434  df-in 3894  df-ss 3904  df-scott 41854

This theorem is referenced by:  elscottab  41862