Theorem expt 647

Description: Exportation theorem pm3.3 259 (closed form of ex 114) expressed with primitive connectives. (Contributed by NM, 5-Aug-1993.)

Assertion

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

Proof of Theorem expt

Step	Hyp	Ref	Expression
1		pm3.2im 627	. . 3 |- ( ph -> ( ps -> -. ( ph -> -. ps ) ) )
2	1	imim1d 75	. 2 |- ( ph -> ( ( -. ( ph -> -. ps ) -> ch ) -> ( ps -> ch ) ) )
3	2	com12 30	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-in1 604  ax-in2 605

This theorem is referenced by: (None)