Theorem scottss 44255

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 44248	. 2 ⊢ Scott 𝐴 = {𝑥 ∈ 𝐴 ∣ ∀𝑦 ∈ 𝐴 (rank‘𝑥) ⊆ (rank‘𝑦)}
2	1	ssrab3 4030	1 ⊢ Scott 𝐴 ⊆ 𝐴

Syntax hints:  ∀wral 3045   ⊆ wss 3900  ‘cfv 6477  rankcrnk 9648  Scott cscott 44247

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2112  ax-9 2120  ax-ext 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1781  df-sb 2067  df-clab 2709  df-cleq 2722  df-clel 2804  df-rab 3394  df-ss 3917  df-scott 44248

This theorem is referenced by:  elscottab  44256