Theorem tbwlem5

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.)

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

Proof

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