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Theorem expt 148
Description: Exportation theorem expressed with primitive connectives. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
expt  |-  ( ( -.  ( ph  ->  -. 
ps )  ->  ch )  ->  ( ph  ->  ( ps  ->  ch )
) )

Proof of Theorem expt
StepHypRef Expression
1 pm3.2im 137 . . 3  |-  ( ph  ->  ( ps  ->  -.  ( ph  ->  -.  ps )
) )
21imim1d 69 . 2  |-  ( ph  ->  ( ( -.  ( ph  ->  -.  ps )  ->  ch )  ->  ( ps  ->  ch ) ) )
32com12 27 1  |-  ( ( -.  ( ph  ->  -. 
ps )  ->  ch )  ->  ( ph  ->  ( ps  ->  ch )
) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
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