Theorem omhf

Description: Finite ordinals are hereditarily finite sets. (Contributed by Eric Schmidt, 26-Sep-2026)

	Ref	Expression
Assertion	omhf	Could not format assertion : No typesetting found for |- ( A e. _om -> A e. HF ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		eleq1	Could not format ( x = (/) -> ( x e. HF <-> (/) e. HF ) ) : No typesetting found for |- ( x = (/) -> ( x e. HF <-> (/) e. HF ) ) with typecode |-
2		eleq1	Could not format ( x = y -> ( x e. HF <-> y e. HF ) ) : No typesetting found for |- ( x = y -> ( x e. HF <-> y e. HF ) ) with typecode |-
3		eleq1	Could not format ( x = suc y -> ( x e. HF <-> suc y e. HF ) ) : No typesetting found for |- ( x = suc y -> ( x e. HF <-> suc y e. HF ) ) with typecode |-
4		eleq1	Could not format ( x = A -> ( x e. HF <-> A e. HF ) ) : No typesetting found for |- ( x = A -> ( x e. HF <-> A e. HF ) ) with typecode |-
5		0hf	Could not format (/) e. HF : No typesetting found for |- (/) e. HF with typecode |-
6		df-suc	$$⊢\mathrm{suc}y=y\cup \left\{y\right\}$$
7		hfadj	Could not format ( ( y e. HF /\ y e. HF ) -> ( y u. { y } ) e. HF ) : No typesetting found for |- ( ( y e. HF /\ y e. HF ) -> ( y u. { y } ) e. HF ) with typecode |-
8	7	anidms	Could not format ( y e. HF -> ( y u. { y } ) e. HF ) : No typesetting found for |- ( y e. HF -> ( y u. { y } ) e. HF ) with typecode |-
9	6 8	eqeltrid	Could not format ( y e. HF -> suc y e. HF ) : No typesetting found for |- ( y e. HF -> suc y e. HF ) with typecode |-
10	9	a1i	Could not format ( y e. _om -> ( y e. HF -> suc y e. HF ) ) : No typesetting found for |- ( y e. _om -> ( y e. HF -> suc y e. HF ) ) with typecode |-
11	1 2 3 4 5 10	finds	Could not format ( A e. _om -> A e. HF ) : No typesetting found for |- ( A e. _om -> A e. HF ) with typecode |-