Theorem jad 165

Description: Deduction form of ja 164. (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 32	. . 3 |- ( -. ps -> ( ph -> th ) )
3		jad.2	. . . 4 |- ( ph -> ( ch -> th ) )
4	3	com12 32	. . 3 |- ( ch -> ( ph -> th ) )
5	2, 4	ja 164	. 2 |- ( ( ps -> ch ) -> ( ph -> th ) )
6	5	com12 32	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  173  pm2.65  175  merco2  1615  wereu2  4846  isfin7-2  8826  axpowndlem3  9024  suppssfz  12205  lo1bdd2  13575  pntlem3  24433  hbimtg  30447  arg-ax  31068  onsuct0  31093  ordcmp  31099  wl-embantd  31761  poimirlem26  31879  ax12indi  32433  hbimpg  36778