Theorem hfelhfOLD

Description: Obsolete version of elhf3 as of 17-Sep-2026. (Contributed by Scott Fenton, 16-Jul-2015) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	hfelhfOLD	Could not format assertion : No typesetting found for |- ( ( A e. B /\ B e. HF ) -> A e. HF ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		rankelg	Could not format ( ( B e. HF /\ A e. B ) -> ( rank ` A ) e. ( rank ` B ) ) : No typesetting found for |- ( ( B e. HF /\ A e. B ) -> ( rank ` A ) e. ( rank ` B ) ) with typecode |-
2	1	ancoms	Could not format ( ( A e. B /\ B e. HF ) -> ( rank ` A ) e. ( rank ` B ) ) : No typesetting found for |- ( ( A e. B /\ B e. HF ) -> ( rank ` A ) e. ( rank ` B ) ) with typecode |-
3		elhf2g	Could not format ( B e. HF -> ( B e. HF <-> ( rank ` B ) e. _om ) ) : No typesetting found for |- ( B e. HF -> ( B e. HF <-> ( rank ` B ) e. _om ) ) with typecode |-
4	3	ibi	Could not format ( B e. HF -> ( rank ` B ) e. _om ) : No typesetting found for |- ( B e. HF -> ( rank ` B ) e. _om ) with typecode |-
5		elnn	$$⊢\left(\mathrm{rank}\left(A\right)\in \mathrm{rank}\left(B\right)\wedge \mathrm{rank}\left(B\right)\in \mathrm{\omega }\right)\to \mathrm{rank}\left(A\right)\in \mathrm{\omega }$$
6		elhf2g	Could not format ( A e. B -> ( A e. HF <-> ( rank ` A ) e. _om ) ) : No typesetting found for |- ( A e. B -> ( A e. HF <-> ( rank ` A ) e. _om ) ) with typecode |-
7	5 6	imbitrrid	Could not format ( A e. B -> ( ( ( rank ` A ) e. ( rank ` B ) /\ ( rank ` B ) e. _om ) -> A e. HF ) ) : No typesetting found for |- ( A e. B -> ( ( ( rank ` A ) e. ( rank ` B ) /\ ( rank ` B ) e. _om ) -> A e. HF ) ) with typecode |-
8	7	expcomd	Could not format ( A e. B -> ( ( rank ` B ) e. _om -> ( ( rank ` A ) e. ( rank ` B ) -> A e. HF ) ) ) : No typesetting found for |- ( A e. B -> ( ( rank ` B ) e. _om -> ( ( rank ` A ) e. ( rank ` B ) -> A e. HF ) ) ) with typecode |-
9	8	imp	Could not format ( ( A e. B /\ ( rank ` B ) e. _om ) -> ( ( rank ` A ) e. ( rank ` B ) -> A e. HF ) ) : No typesetting found for |- ( ( A e. B /\ ( rank ` B ) e. _om ) -> ( ( rank ` A ) e. ( rank ` B ) -> A e. HF ) ) with typecode |-
10	4 9	sylan2	Could not format ( ( A e. B /\ B e. HF ) -> ( ( rank ` A ) e. ( rank ` B ) -> A e. HF ) ) : No typesetting found for |- ( ( A e. B /\ B e. HF ) -> ( ( rank ` A ) e. ( rank ` B ) -> A e. HF ) ) with typecode |-
11	2 10	mpd	Could not format ( ( A e. B /\ B e. HF ) -> A e. HF ) : No typesetting found for |- ( ( A e. B /\ B e. HF ) -> A e. HF ) with typecode |-