Theorem impt 149

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

Step	Hyp	Ref	Expression
1		simprim 142	. 2 |- (-. (ph -> -. ps) -> ps)
2		simplim 143	. . 3 |- (-. (ph -> -. ps) -> ph)
3	2	imim1i 54	. 2 |- ((ph -> (ps -> ch)) -> (-. (ph -> -. ps) -> (ps -> ch)))
4	1, 3	mpdi 38	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)