Theorem r1omtsk

Description: The set of hereditarily finite sets is a Tarski class. (The Tarski-Grothendieck Axiom is not needed for this theorem.) (Contributed by Mario Carneiro, 28-May-2013)

	Ref	Expression
Assertion	r1omtsk	⊢ ( 𝑅1 ‘ ω ) ∈ Tarski

Proof

Step	Hyp	Ref	Expression
1		omina	⊢ ω ∈ Inacc
2		inatsk	⊢ ( ω ∈ Inacc → ( 𝑅1 ‘ ω ) ∈ Tarski )
3	1 2	ax-mp	⊢ ( 𝑅1 ‘ ω ) ∈ Tarski