Theorem hbimdOLD 1816

Description: Obsolete proof of hbimd 1815 as of 16-Dec-2017. (Contributed by NM, 1-Jan-2002.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
hbimd.1	|- (ph -> A.xph)
hbimd.2	|- (ph -> (ps -> A.xps))
hbimd.3	|- (ph -> (ch -> A.xch))

Assertion

Ref	Expression
hbimdOLD	|- (ph -> ((ps -> ch) -> A.x(ps -> ch)))

Proof of Theorem hbimdOLD

Step	Hyp	Ref	Expression
1		hbimd.1	. . . . 5 |- (ph -> A.xph)
2		hbimd.2	. . . . 5 |- (ph -> (ps -> A.xps))
3	1, 2	alrimih 1565	. . . 4 |- (ph -> A.x(ps -> A.xps))
4		sp 1747	. . . . . 6 |- (A.xps -> ps)
5		hbn1 1730	. . . . . 6 |- (-. A.xps -> A.x -. A.xps)
6	4, 5	nsyl4 134	. . . . 5 |- (-. A.x -. A.xps -> ps)
7	6	con1i 121	. . . 4 |- (-. ps -> A.x -. A.xps)
8		con3 126	. . . . 5 |- ((ps -> A.xps) -> (-. A.xps -> -. ps))
9	8	al2imi 1561	. . . 4 |- (A.x(ps -> A.xps) -> (A.x -. A.xps -> A.x -. ps))
10	3, 7, 9	syl2im 34	. . 3 |- (ph -> (-. ps -> A.x -. ps))
11		pm2.21 100	. . . 4 |- (-. ps -> (ps -> ch))
12	11	alimi 1559	. . 3 |- (A.x -. ps -> A.x(ps -> ch))
13	10, 12	syl6 29	. 2 |- (ph -> (-. ps -> A.x(ps -> ch)))
14		hbimd.3	. . 3 |- (ph -> (ch -> A.xch))
15		ax-1 6	. . . 4 |- (ch -> (ps -> ch))
16	15	alimi 1559	. . 3 |- (A.xch -> A.x(ps -> ch))
17	14, 16	syl6 29	. 2 |- (ph -> (ch -> A.x(ps -> ch)))
18	13, 17	jad 154	1 |- (ph -> ((ps -> ch) -> A.x(ps -> ch)))

Syntax hints:  -. wn 3   -> wi 4  A.wal 1540

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

This theorem is referenced by: (None)