Theorem pm4.8 623

Description: Theorem *4.8 of [WhiteheadRussell] p. 122. This one holds for all propositions, but compare with pm4.81dc 814 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		pm2.01 546	. 2 |- ( ( ph -> -. ph ) -> -. ph )
2		ax-1 5	. 2 |- ( -. ph -> ( ph -> -. ph ) )
3	1, 2	impbii 117	1 |- ( ( ph -> -. ph ) <-> -. ph )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 100  ax-ia3 101  ax-in1 544

This theorem depends on definitions:  df-bi 110

This theorem is referenced by: (None)