Theorem nfaldOLD 2166

Description: Obsolete proof of nfald 2165 as of 16-Oct-2021. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 6-Jan-2018.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
nfald.1	|- F/ y ph
nfald.2	|- ( ph -> F/ x ps )

Assertion

Ref	Expression
nfaldOLD	|- ( ph -> F/ x A. y ps )

Proof of Theorem nfaldOLD

Step	Hyp	Ref	Expression
1		nfald.1	. . 3 |- F/ y ph
2		nfald.2	. . 3 |- ( ph -> F/ x ps )
3	1, 2	alrimi 2082	. 2 |- ( ph -> A. y F/ x ps )
4		nfnf1 2031	. . . 4 |- F/ x F/ x ps
5	4	nfal 2153	. . 3 |- F/ x A. y F/ x ps
6		hba1 2151	. . . 4 |- ( A. y F/ x ps -> A. y A. y F/ x ps )
7		sp 2053	. . . . 5 |- ( A. y F/ x ps -> F/ x ps )
8	7	nf5rd 2066	. . . 4 |- ( A. y F/ x ps -> ( ps -> A. x ps ) )
9	6, 8	hbald 2041	. . 3 |- ( A. y F/ x ps -> ( A. y ps -> A. x A. y ps ) )
10	5, 9	nf5d 2118	. 2 |- ( A. y F/ x ps -> F/ x A. y ps )
11	3, 10	syl 17	1 |- ( ph -> F/ x A. y ps )

Syntax hints:   -> wi 4   A.wal 1481   F/wnf 1708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-11 2034  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710

This theorem is referenced by: (None)