Theorem re1luk2 1476

Description: luk-2 1421 derived from the Tarski-Bernays-Wajsberg axioms. (Contributed by Anthony Hart, 16-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
re1luk2	|- ((-. ph -> ph) -> ph)

Proof of Theorem re1luk2

Step	Hyp	Ref	Expression
1		tbw-negdf 1464	. . . 4 |- (((-. ph -> (ph -> F. )) -> (((ph -> F. ) -> -. ph) -> F. )) -> F. )
2		tbw-ax2 1466	. . . . 5 |- ((((ph -> F. ) -> -. ph) -> F. ) -> ((-. ph -> (ph -> F. )) -> (((ph -> F. ) -> -. ph) -> F. )))
3		tbwlem4 1473	. . . . 5 |- (((((ph -> F. ) -> -. ph) -> F. ) -> ((-. ph -> (ph -> F. )) -> (((ph -> F. ) -> -. ph) -> F. ))) -> ((((-. ph -> (ph -> F. )) -> (((ph -> F. ) -> -. ph) -> F. )) -> F. ) -> ((ph -> F. ) -> -. ph)))
4	2, 3	ax-mp 5	. . . 4 |- ((((-. ph -> (ph -> F. )) -> (((ph -> F. ) -> -. ph) -> F. )) -> F. ) -> ((ph -> F. ) -> -. ph))
5	1, 4	ax-mp 5	. . 3 |- ((ph -> F. ) -> -. ph)
6		tbw-ax1 1465	. . 3 |- (((ph -> F. ) -> -. ph) -> ((-. ph -> ph) -> ((ph -> F. ) -> ph)))
7	5, 6	ax-mp 5	. 2 |- ((-. ph -> ph) -> ((ph -> F. ) -> ph))
8		tbw-ax3 1467	. 2 |- (((ph -> F. ) -> ph) -> ph)
9	7, 8	tbwsyl 1469	1 |- ((-. ph -> ph) -> ph)

Syntax hints:  -. wn 3   -> wi 4   F. wfal 1317

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-tru 1319  df-fal 1320

This theorem is referenced by: (None)