Theorem re1tbw3 1672

Description: tbw-ax3 1627 rederived from merco2 1661. (Contributed by Anthony Hart, 16-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

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

Proof of Theorem re1tbw3

Step	Hyp	Ref	Expression
1		mercolem2 1663	. 2 |- ( ( ( ph -> ph ) -> ph ) -> ( ph -> ( ph -> ph ) ) )
2		mercolem2 1663	. . 3 |- ( ( ( ph -> ps ) -> ph ) -> ( ( ( ( ph -> ph ) -> ph ) -> ( ph -> ( ph -> ph ) ) ) -> ( ( ( ph -> ps ) -> ph ) -> ph ) ) )
3		mercolem6 1667	. . 3 |- ( ( ( ( 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 5	. 2 |- ( ( ( ( ph -> ph ) -> ph ) -> ( ph -> ( ph -> ph ) ) ) -> ( ( ( ph -> ps ) -> ph ) -> ph ) )
5	1, 4	ax-mp 5	1 |- ( ( ( ph -> ps ) -> ph ) -> ph )

Syntax hints:   -> wi 4

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 197  df-tru 1486  df-fal 1489

This theorem is referenced by:  re1tbw4  1673