Theorem hfpwOLD

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

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

Proof

Step	Hyp	Ref	Expression
1		rankpwg	Could not format ( A e. HF -> ( rank ` ~P A ) = suc ( rank ` A ) ) : No typesetting found for |- ( A e. HF -> ( rank ` ~P 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 ` ~P A ) e. _om ) : No typesetting found for |- ( A e. HF -> ( rank ` ~P A ) e. _om ) with typecode |-
7		pwexg	Could not format ( A e. HF -> ~P A e. _V ) : No typesetting found for |- ( A e. HF -> ~P A e. _V ) with typecode |-
8		elhf2g	Could not format ( ~P A e. _V -> ( ~P A e. HF <-> ( rank ` ~P A ) e. _om ) ) : No typesetting found for |- ( ~P A e. _V -> ( ~P A e. HF <-> ( rank ` ~P A ) e. _om ) ) with typecode |-
9	7 8	syl	Could not format ( A e. HF -> ( ~P A e. HF <-> ( rank ` ~P A ) e. _om ) ) : No typesetting found for |- ( A e. HF -> ( ~P A e. HF <-> ( rank ` ~P A ) e. _om ) ) with typecode |-
10	6 9	mpbird	Could not format ( A e. HF -> ~P A e. HF ) : No typesetting found for |- ( A e. HF -> ~P A e. HF ) with typecode |-