Theorem nfndOLD 1792

Description: Obsolete proof of nfnd 1791 as of 28-Dec-2017. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
nfnd.1	|- (ph -> F/xps)

Assertion

Ref	Expression
nfndOLD	|- (ph -> F/x -. ps)

Proof of Theorem nfndOLD

Step	Hyp	Ref	Expression
1		nfnd.1	. 2 |- (ph -> F/xps)
2		nfnf1 1790	. . 3 |- F/x F/xps
3		ax6o 1750	. . . . 5 |- (-. A.x -. A.xps -> ps)
4	3	con1i 121	. . . 4 |- (-. ps -> A.x -. A.xps)
5		df-nf 1545	. . . . 5 |- ( F/xps <-> A.x(ps -> A.xps))
6		con3 126	. . . . . 6 |- ((ps -> A.xps) -> (-. A.xps -> -. ps))
7	6	al2imi 1561	. . . . 5 |- (A.x(ps -> A.xps) -> (A.x -. A.xps -> A.x -. ps))
8	5, 7	sylbi 187	. . . 4 |- ( F/xps -> (A.x -. A.xps -> A.x -. ps))
9	4, 8	syl5 28	. . 3 |- ( F/xps -> (-. ps -> A.x -. ps))
10	2, 9	nfd 1766	. 2 |- ( F/xps -> F/x -. ps)
11	1, 10	syl 15	1 |- (ph -> F/x -. ps)

Syntax hints:  -. wn 3   -> wi 4  A.wal 1540   F/wnf 1544

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545

This theorem is referenced by: (None)