Theorem impt 169

Description: Importation theorem imp 445 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

Step	Hyp	Ref	Expression
1		simprim 162	. 2 |- ( -. ( ph -> -. ps ) -> ps )
2		simplim 163	. . 3 |- ( -. ( ph -> -. ps ) -> ph )
3	2	imim1i 63	. 2 |- ( ( ph -> ( ps -> ch ) ) -> ( -. ( ph -> -. ps ) -> ( ps -> ch ) ) )
4	1, 3	mpdi 45	1 |- ( ( ph -> ( ps -> ch ) ) -> ( -. ( ph -> -. ps ) -> ch ) )

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: (None)