Theorem hfsnOLD

Description: Obsolete version of hfsn as of 17-Sep-2026. (Contributed by Scott Fenton, 15-Jul-2015) (Proof modification is discouraged.) (New usage is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		ranksng	Could not format ( A e. HF -> ( rank ` { A } ) = suc ( rank ` A ) ) : No typesetting found for |- ( A e. HF -> ( rank ` { A } ) = suc ( rank ` A ) ) with typecode |-
2		elhf2g	Could not format ( A e. HF -> ( A e. HF <-> ( rank ` A ) e. _om ) ) : No typesetting found for |- ( A e. HF -> ( A e. HF <-> ( rank ` A ) e. _om ) ) with typecode |-
3	2	ibi	Could not format ( A e. HF -> ( rank ` A ) e. _om ) : No typesetting found for |- ( A e. HF -> ( rank ` A ) e. _om ) with typecode |-
4		peano2	$$⊢\mathrm{rank}\left(A\right)\in \mathrm{\omega }\to \mathrm{suc}\mathrm{rank}\left(A\right)\in \mathrm{\omega }$$
5	3 4	syl	Could not format ( A e. HF -> suc ( rank ` A ) e. _om ) : No typesetting found for |- ( A e. HF -> suc ( rank ` A ) e. _om ) with typecode |-
6	1 5	eqeltrd	Could not format ( A e. HF -> ( rank ` { A } ) e. _om ) : No typesetting found for |- ( A e. HF -> ( rank ` { A } ) e. _om ) with typecode |-
7		snex	$$⊢\left\{A\right\}\in \mathrm{V}$$
8	7	elhf2	Could not format ( { A } e. HF <-> ( rank ` { A } ) e. _om ) : No typesetting found for |- ( { A } e. HF <-> ( rank ` { A } ) e. _om ) with typecode |-
9	6 8	sylibr	Could not format ( A e. HF -> { A } e. HF ) : No typesetting found for |- ( A e. HF -> { A } e. HF ) with typecode |-