Theorem re1tbw2

Description: tbw-ax2 rederived from merco2 . (Contributed by Anthony Hart, 16-Aug-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	re1tbw2	|- ( ph -> ( ps -> ph ) )

Proof

Step	Hyp	Ref	Expression
1		mercolem1	|- ( ( ( ph -> ph ) -> ph ) -> ( ph -> ( ps -> ph ) ) )
2		mercolem1	|- ( ( ( ( ph -> ph ) -> ph ) -> ( ph -> ( ps -> ph ) ) ) -> ( ph -> ( ps -> ( ph -> ( ps -> ph ) ) ) ) )
3	1 2	ax-mp	|- ( ph -> ( ps -> ( ph -> ( ps -> ph ) ) ) )
4		mercolem6	|- ( ( ph -> ( ps -> ( ph -> ( ps -> ph ) ) ) ) -> ( ps -> ( ph -> ( ps -> ph ) ) ) )
5	3 4	ax-mp	|- ( ps -> ( ph -> ( ps -> ph ) ) )
6		mercolem6	|- ( ( ps -> ( ph -> ( ps -> ph ) ) ) -> ( ph -> ( ps -> ph ) ) )
7	5 6	ax-mp	|- ( ph -> ( ps -> ph ) )