Theorem simprim 162

Description: Simplification. Similar to Theorem *3.27 (Simp) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-1993.) (Proof shortened by Wolf Lammen, 13-Nov-2012.)

Assertion

Ref	Expression
simprim	|- ( -. ( ph -> -. ps ) -> ps )

Proof of Theorem simprim

Step	Hyp	Ref	Expression
1		idd 24	. 2 |- ( ph -> ( ps -> ps ) )
2	1	impi 160	1 |- ( -. ( ph -> -. ps ) -> ps )

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:  impt  169  impbi  198  biimpr  210  imbi12  336