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 = U. ( R1 " _om )

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		chf	|- HF
1		cr1	|- R1
2		com	|- _om
3	1 2	cima	|- ( R1 " _om )
4	3	cuni	|- U. ( R1 " _om )
5	0 4	wceq	|- HF = U. ( R1 " _om )