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Theorem impt 151
Description: Importation theorem expressed with primitive connectives. (Contributed by NM, 25-Apr-1994.) (Proof shortened by Wolf Lammen, 20-Jul-2013.)
Assertion
Ref Expression
impt  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  ( -.  ( ph  ->  -.  ps )  ->  ch )
)

Proof of Theorem impt
StepHypRef Expression
1 simprim 144 . 2  |-  ( -.  ( ph  ->  -.  ps )  ->  ps )
2 simplim 145 . . 3  |-  ( -.  ( ph  ->  -.  ps )  ->  ph )
32imim1i 56 . 2  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  ( -.  ( ph  ->  -.  ps )  ->  ( ps 
->  ch ) ) )
41, 3mpdi 40 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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