Theorem tbw-negdf 14166

Description: The definition of negation, in terms of -> and F..

Assertion

Ref	Expression
tbw-negdf	|- (((-. ph -> (ph -> F. )) -> (((ph -> F. ) -> -. ph) -> F. )) -> F. )

Proof of Theorem tbw-negdf

Step	Hyp	Ref	Expression
1		pm2.21 92	. . 3 |- (-. ph -> (ph -> F. ))
2		ax-1 4	. . . . 5 |- (-. ph -> ((ph -> F. ) -> -. ph))
3		FiA 14104	. . . . 5 |- ( F. -> ((ph -> F. ) -> -. ph))
4	2, 3	ja 152	. . . 4 |- ((ph -> F. ) -> ((ph -> F. ) -> -. ph))
5	4	pm2.43i 78	. . 3 |- ((ph -> F. ) -> -. ph)
6	1, 5	impbii 174	. 2 |- (-. ph <-> (ph -> F. ))
7		tbw-bijust 14165	. 2 |- ((-. ph <-> (ph -> F. )) <-> (((-. ph -> (ph -> F. )) -> (((ph -> F. ) -> -. ph) -> F. )) -> F. ))
8	6, 7	mpbi 206	1 |- (((-. ph -> (ph -> F. )) -> (((ph -> F. ) -> -. ph) -> F. )) -> F. )

Syntax hints:  -. wn 2   -> wi 3   <-> wb 163   F. wfal 1261

This theorem is referenced by:  re1luk2 14178  re1luk3 14179

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 164  df-tru 1262  df-fal 1263

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