Theorem scottss

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

	Ref	Expression
Assertion	scottss	⊢ Scott 𝐴 ⊆ 𝐴

Proof

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