Theorem impt 141

Description: Importation theorem expressed with primitive connectives.

Assertion

Ref	Expression
impt	|- ((ph -> (ps -> ch)) -> (-. (ph -> -. ps) -> ch))

Proof of Theorem impt

Step	Hyp	Ref	Expression
1		con3 94	. . . 4 |- ((ps -> ch) -> (-. ch -> -. ps))
2	1	imim2i 17	. . 3 |- ((ph -> (ps -> ch)) -> (ph -> (-. ch -> -. ps)))
3	2	com23 32	. 2 |- ((ph -> (ps -> ch)) -> (-. ch -> (ph -> -. ps)))
4	3	con1d 93	1 |- ((ph -> (ps -> ch)) -> (-. (ph -> -. ps) -> ch))

Syntax hints:  -. wn 2   -> wi 3

This theorem is referenced by:  impi 143  impexp 347

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

Copyright terms: Public domain