Theorem nfimdOLD 2226

Description: Obsolete proof of nfimd 1823 as of 6-Oct-2021. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 30-Dec-2017.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
nfimdOLD.1	|- ( ph -> F/ x ps )
nfimdOLD.2	|- ( ph -> F/ x ch )

Assertion

Ref	Expression
nfimdOLD	|- ( ph -> F/ x ( ps -> ch ) )

Proof of Theorem nfimdOLD

Step	Hyp	Ref	Expression
1		nfimdOLD.1	. 2 |- ( ph -> F/ x ps )
2		nfimdOLD.2	. 2 |- ( ph -> F/ x ch )
3		nfnf1OLDOLD 2208	. . . 4 |- F/ x F/ x ps
4		nfnf1OLDOLD 2208	. . . 4 |- F/ x F/ x ch
5		nfrOLD 2188	. . . . . 6 |- ( F/ x ch -> ( ch -> A. x ch ) )
6	5	imim2d 57	. . . . 5 |- ( F/ x ch -> ( ( ps -> ch ) -> ( ps -> A. x ch ) ) )
7		19.21tOLD 2213	. . . . . 6 |- ( F/ x ps -> ( A. x ( ps -> ch ) <-> ( ps -> A. x ch ) ) )
8	7	biimprd 238	. . . . 5 |- ( F/ x ps -> ( ( ps -> A. x ch ) -> A. x ( ps -> ch ) ) )
9	6, 8	syl9r 78	. . . 4 |- ( F/ x ps -> ( F/ x ch -> ( ( ps -> ch ) -> A. x ( ps -> ch ) ) ) )
10	3, 4, 9	alrimdOLD 2196	. . 3 |- ( F/ x ps -> ( F/ x ch -> A. x ( ( ps -> ch ) -> A. x ( ps -> ch ) ) ) )
11		df-nfOLD 1721	. . 3 |- ( F/ x ( ps -> ch ) <-> A. x ( ( ps -> ch ) -> A. x ( ps -> ch ) ) )
12	10, 11	syl6ibr 242	. 2 |- ( F/ x ps -> ( F/ x ch -> F/ x ( ps -> ch ) ) )
13	1, 2, 12	sylc 65	1 |- ( ph -> F/ x ( ps -> ch ) )

Syntax hints:   -> wi 4   A.wal 1481   F/wnfOLD 1709

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-12 2047

This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1705  df-nf 1710  df-nfOLD 1721

This theorem is referenced by:  hbimdOLD  2230  nfandOLD  2232  nfbidOLD  2242