Theorem jadOLD2 157

Description: Deduction form of ja 152. (Contributed by Scott Fenton, 13-Dec-2010.)

Hypotheses

Ref	Expression
jad.1	|- (ph -> (-. ps -> th))
jad.2	|- (ph -> (ch -> th))

Assertion

Ref	Expression
jadOLD2	|- (ph -> ((ps -> ch) -> th))

Proof of Theorem jadOLD2

Step	Hyp	Ref	Expression
1		jad.1	. . 3 |- (ph -> (-. ps -> th))
2	1	imim2d 28	. 2 |- (ph -> (((ps -> ch) -> -. ps) -> ((ps -> ch) -> th)))
3		pm2.27 76	. . . 4 |- (ps -> ((ps -> ch) -> ch))
4		jad.2	. . . 4 |- (ph -> (ch -> th))
5	3, 4	syl9r 72	. . 3 |- (ph -> (ps -> ((ps -> ch) -> th)))
6		simprim 155	. . 3 |- (-. ((ps -> ch) -> -. ps) -> ps)
7	5, 6	syl5 20	. 2 |- (ph -> (-. ((ps -> ch) -> -. ps) -> ((ps -> ch) -> th)))
8	2, 7	pm2.61d 141	1 |- (ph -> ((ps -> ch) -> th))

Syntax hints:  -. wn 2   -> wi 3

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

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