Theorem tbwlem5 1474

Description: Used to rederive the Lukasiewicz axioms from Tarski-Bernays-Wajsberg'. (Contributed by Anthony Hart, 16-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
tbwlem5	|- (((ph -> (ps -> F. )) -> F. ) -> ph)

Proof of Theorem tbwlem5

Step	Hyp	Ref	Expression
1		tbw-ax2 1466	. . . 4 |- (ph -> (ps -> ph))
2		tbw-ax1 1465	. . . 4 |- ((ps -> ph) -> ((ph -> F. ) -> (ps -> F. )))
3	1, 2	tbwsyl 1469	. . 3 |- (ph -> ((ph -> F. ) -> (ps -> F. )))
4		tbwlem1 1470	. . 3 |- ((ph -> ((ph -> F. ) -> (ps -> F. ))) -> ((ph -> F. ) -> (ph -> (ps -> F. ))))
5	3, 4	ax-mp 5	. 2 |- ((ph -> F. ) -> (ph -> (ps -> F. )))
6		tbwlem4 1473	. 2 |- (((ph -> F. ) -> (ph -> (ps -> F. ))) -> (((ph -> (ps -> F. )) -> F. ) -> ph))
7	5, 6	ax-mp 5	1 |- (((ph -> (ps -> F. )) -> F. ) -> ph)

Syntax hints:   -> 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:  re1luk3  1477