Theorem pm4.8 696

Description: Theorem *4.8 of [WhiteheadRussell] p. 122. This one holds for all propositions, but compare with pm4.81dc 893 which requires a decidability condition. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm4.8	|- ( ( ph -> -. ph ) <-> -. ph )

Proof of Theorem pm4.8

Step	Hyp	Ref	Expression
1		pm2.01 605	. 2 |- ( ( ph -> -. ph ) -> -. ph )
2		ax-1 6	. 2 |- ( -. ph -> ( ph -> -. ph ) )
3	1, 2	impbii 125	1 |- ( ( ph -> -. ph ) <-> -. ph )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 106  ax-ia3 107  ax-in1 603

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)