Theorem re1tbw2 1671

Description: tbw-ax2 1626 rederived from merco2 1661. (Contributed by Anthony Hart, 16-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

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

Proof of Theorem re1tbw2

Step	Hyp	Ref	Expression
1		mercolem1 1662	. . . 4 |- ( ( ( ph -> ph ) -> ph ) -> ( ph -> ( ps -> ph ) ) )
2		mercolem1 1662	. . . 4 |- ( ( ( ( ph -> ph ) -> ph ) -> ( ph -> ( ps -> ph ) ) ) -> ( ph -> ( ps -> ( ph -> ( ps -> ph ) ) ) ) )
3	1, 2	ax-mp 5	. . 3 |- ( ph -> ( ps -> ( ph -> ( ps -> ph ) ) ) )
4		mercolem6 1667	. . 3 |- ( ( ph -> ( ps -> ( ph -> ( ps -> ph ) ) ) ) -> ( ps -> ( ph -> ( ps -> ph ) ) ) )
5	3, 4	ax-mp 5	. 2 |- ( ps -> ( ph -> ( ps -> ph ) ) )
6		mercolem6 1667	. 2 |- ( ( ps -> ( ph -> ( ps -> ph ) ) ) -> ( ph -> ( ps -> ph ) ) )
7	5, 6	ax-mp 5	1 |- ( ph -> ( ps -> 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  ltrneq  35435