Theorem impt 122

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 86	. . . 4 |- ((ps -> ch) -> (-. ch -> -. ps))
2	1	syl3 18	. . 3 |- ((ph -> (ps -> ch)) -> (ph -> (-. ch -> -. ps)))
3	2	com23 32	. 2 |- ((ph -> (ps -> ch)) -> (-. ch -> (ph -> -. ps)))
4	3	con1d 85	1 |- ((ph -> (ps -> ch)) -> (-. (ph -> -. ps) -> ch))

Syntax hints:  -. wn 1   -> wi 2

This theorem is referenced by:  impi 124  impexp 276

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

metamath.org