Definition df-hf

Description: Define the class of sets belonging to the finite stages of the cumulative hierarchy of sets. This is the class of sets of finite rank by elhf2 . They are called the hereditarily finite sets since they are the finite sets whose members are hereditarily finite, as proved in elhf3 . (Contributed by Scott Fenton, 9-Jul-2015)

	Ref	Expression
Assertion	df-hf	⊢ HF = ∪ ( 𝑅1 “ ω )

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		chf	⊢ HF
1		cr1	⊢ 𝑅1
2		com	⊢ ω
3	1 2	cima	⊢ ( 𝑅1 “ ω )
4	3	cuni	⊢ ∪ ( 𝑅1 “ ω )
5	0 4	wceq	⊢ HF = ∪ ( 𝑅1 “ ω )