Theorem re1luk2 15125

Description: luk-2 1520 derived from the Tarski-Bernays-Wajsberg axioms.

Assertion

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

Proof of Theorem re1luk2

Step	Hyp	Ref	Expression
1		tbw-negdf 15113	. . . 4 |- (((-. ph -> (ph -> F. )) -> (((ph -> F. ) -> -. ph) -> F. )) -> F. )
2		tbw-ax2 15115	. . . . 5 |- ((((ph -> F. ) -> -. ph) -> F. ) -> ((-. ph -> (ph -> F. )) -> (((ph -> F. ) -> -. ph) -> F. )))
3		tbwlem4 15122	. . . . 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 7	. . . 4 |- ((((-. ph -> (ph -> F. )) -> (((ph -> F. ) -> -. ph) -> F. )) -> F. ) -> ((ph -> F. ) -> -. ph))
5	1, 4	ax-mp 7	. . 3 |- ((ph -> F. ) -> -. ph)
6		tbw-ax1 15114	. . 3 |- (((ph -> F. ) -> -. ph) -> ((-. ph -> ph) -> ((ph -> F. ) -> ph)))
7	5, 6	ax-mp 7	. 2 |- ((-. ph -> ph) -> ((ph -> F. ) -> ph))
8		tbw-ax3 15116	. 2 |- (((ph -> F. ) -> ph) -> ph)
9	7, 8	tbwsyl 15118	1 |- ((-. ph -> ph) -> ph)

Syntax hints:  -. wn 2   -> wi 3   F. wfal 1565

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 232  df-tru 1566  df-fal 1567

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