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Theorem expt 593
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 576 . . 3  |-  ( ph  ->  ( ps  ->  -.  ( ph  ->  -.  ps )
) )
21imim1d 73 . 2  |-  ( ph  ->  ( ( -.  ( ph  ->  -.  ps )  ->  ch )  ->  ( ps  ->  ch ) ) )
32com12 30 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-mp 7  ax-in1 554  ax-in2 555
This theorem is referenced by: (None)
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