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Theorem jad 162
Description: Deduction form of ja 161. (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 31 . . 3  |-  ( -. 
ps  ->  ( ph  ->  th ) )
3 jad.2 . . . 4  |-  ( ph  ->  ( ch  ->  th )
)
43com12 31 . . 3  |-  ( ch 
->  ( ph  ->  th )
)
52, 4ja 161 . 2  |-  ( ( ps  ->  ch )  ->  ( ph  ->  th )
)
65com12 31 1  |-  ( ph  ->  ( ( ps  ->  ch )  ->  th )
)
Colors of variables: wff setvar class
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  170  pm2.65  172  merco2  1544  ax12indi  2254  wereu2  4826  isfin7-2  8677  axpowndlem3  8876  axpowndlem3OLD  8877  lo1bdd2  13121  pntlem3  22992  hbimtg  27765  arg-ax  28407  onsuct0  28432  ordcmp  28438  wl-embantd  28502  suppssfz  30935  hbimpg  31596
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