Theorem jad 154

Description: Deduction form of ja 153. (Contributed by Scott Fenton, 13-Dec-2010.) (Proof shortened by Andrew Salmon, 17-Sep-2011.)

Hypotheses

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

Assertion

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

Proof of Theorem jad

Step	Hyp	Ref	Expression
1		jad.1	. . . 4 |- (ph -> (-. ps -> th))
2	1	com12 27	. . 3 |- (-. ps -> (ph -> th))
3		jad.2	. . . 4 |- (ph -> (ch -> th))
4	3	com12 27	. . 3 |- (ch -> (ph -> th))
5	2, 4	ja 153	. 2 |- ((ps -> ch) -> (ph -> th))
6	5	com12 27	1 |- (ph -> ((ps -> ch) -> th))

Syntax hints:  -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by:  pm2.6  162  pm2.65  164  merco2  1501  nfimdOLD  1809  hbimdOLD  1816  ax11indi  2196