Theorem jad 174

Description: Deduction form of ja 173. (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 173	. 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  182  pm2.65  184  merco2  1661  nfimdOLDOLD  1824  wereu2  5111  isfin7-2  9218  axpowndlem3  9421  suppssfz  12794  lo1bdd2  14255  pntlem3  25298  hbimtg  31712  arg-ax  32415  onsuct0  32440  ordcmp  32446  poimirlem26  33435  ax12indi  34229  ntrneiiso  38389  hbimpg  38770