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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
StepHypRef Expression
1 jad.1 . . . 4  |-  ( ph  ->  ( -.  ps  ->  th ) )
21com12 27 . . 3  |-  ( -. 
ps  ->  ( ph  ->  th ) )
3 jad.2 . . . 4  |-  ( ph  ->  ( ch  ->  th )
)
43com12 27 . . 3  |-  ( ch 
->  ( ph  ->  th )
)
52, 4ja 153 . 2  |-  ( ( ps  ->  ch )  ->  ( ph  ->  th )
)
65com12 27 1  |-  ( ph  ->  ( ( ps  ->  ch )  ->  th )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem is referenced by:  pm2.6  162  pm2.65  164  merco2  1491  hbimd  1721  nfimd  1761  ax11indi  2135  wereu2  4390  isfin7-2  8022  axpowndlem3  8221  lo1bdd2  11998  pntlem3  20758  hbimtg  24163  arg-ax  24855  onsuct0  24880  ordcmp  24886  wl-adnestantd  24908  hbimpg  28320  ax9lem9  29148
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
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