Theorem impi 160

Description: An importation inference. (Contributed by NM, 29-Dec-1992.) (Proof shortened by Wolf Lammen, 20-Jul-2013.)

Hypothesis

Ref	Expression
impi.1	|- ( ph -> ( ps -> ch ) )

Assertion

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

Proof of Theorem impi

Step	Hyp	Ref	Expression
1		impi.1	. . 3 |- ( ph -> ( ps -> ch ) )
2	1	con3rr3 151	. 2 |- ( -. ch -> ( ph -> -. ps ) )
3	2	con1i 144	1 |- ( -. ( 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:  simprim  162  dfbi1  203  imp  445