Theorem scottex2

Description: scottex expressed using Scott . (Contributed by Rohan Ridenour, 9-Aug-2023)

	Ref	Expression
Assertion	scottex2	⊢ Scott 𝐴 ∈ V

Proof

Step	Hyp	Ref	Expression
1		df-scott	⊢ Scott 𝐴 = { 𝑥 ∈ 𝐴 ∣ ∀ 𝑦 ∈ 𝐴 ( rank ‘ 𝑥 ) ⊆ ( rank ‘ 𝑦 ) }
2		scottex	⊢ { 𝑥 ∈ 𝐴 ∣ ∀ 𝑦 ∈ 𝐴 ( rank ‘ 𝑥 ) ⊆ ( rank ‘ 𝑦 ) } ∈ V
3	1 2	eqeltri	⊢ Scott 𝐴 ∈ V