Theorem re1tbw3

Description: tbw-ax3 rederived from merco2 . (Contributed by Anthony Hart, 16-Aug-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	re1tbw3	|- ( ( ( ph -> ps ) -> ph ) -> ph )

Proof

Step	Hyp	Ref	Expression
1		mercolem2	|- ( ( ( ph -> ph ) -> ph ) -> ( ph -> ( ph -> ph ) ) )
2		mercolem2	|- ( ( ( ph -> ps ) -> ph ) -> ( ( ( ( ph -> ph ) -> ph ) -> ( ph -> ( ph -> ph ) ) ) -> ( ( ( ph -> ps ) -> ph ) -> ph ) ) )
3		mercolem6	|- ( ( ( ( ph -> ps ) -> ph ) -> ( ( ( ( ph -> ph ) -> ph ) -> ( ph -> ( ph -> ph ) ) ) -> ( ( ( ph -> ps ) -> ph ) -> ph ) ) ) -> ( ( ( ( ph -> ph ) -> ph ) -> ( ph -> ( ph -> ph ) ) ) -> ( ( ( ph -> ps ) -> ph ) -> ph ) ) )
4	2 3	ax-mp	|- ( ( ( ( ph -> ph ) -> ph ) -> ( ph -> ( ph -> ph ) ) ) -> ( ( ( ph -> ps ) -> ph ) -> ph ) )
5	1 4	ax-mp	|- ( ( ( ph -> ps ) -> ph ) -> ph )