Theorem re1tbw1 1670

Description: tbw-ax1 1625 rederived from merco2 1661. (Contributed by Anthony Hart, 16-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
re1tbw1	|- ( ( ph -> ps ) -> ( ( ps -> ch ) -> ( ph -> ch ) ) )

Proof of Theorem re1tbw1

Step	Hyp	Ref	Expression
1		mercolem8 1669	. . 3 |- ( ( ph -> ps ) -> ( ( ps -> ( ph -> ch ) ) -> ( ( ph -> ps ) -> ( ( ps -> ch ) -> ( ph -> ch ) ) ) ) )
2		mercolem3 1664	. . 3 |- ( ( ps -> ch ) -> ( ps -> ( ph -> ch ) ) )
3		mercolem6 1667	. . 3 |- ( ( ( ph -> ps ) -> ( ( ps -> ( ph -> ch ) ) -> ( ( ph -> ps ) -> ( ( ps -> ch ) -> ( ph -> ch ) ) ) ) ) -> ( ( ps -> ( ph -> ch ) ) -> ( ( ph -> ps ) -> ( ( ps -> ch ) -> ( ph -> ch ) ) ) ) )
4	1, 2, 3	mpsyl 68	. 2 |- ( ( ps -> ch ) -> ( ( ph -> ps ) -> ( ( ps -> ch ) -> ( ph -> ch ) ) ) )
5		mercolem6 1667	. 2 |- ( ( ( ps -> ch ) -> ( ( ph -> ps ) -> ( ( ps -> ch ) -> ( ph -> ch ) ) ) ) -> ( ( ph -> ps ) -> ( ( ps -> ch ) -> ( ph -> ch ) ) ) )
6	4, 5	ax-mp 5	1 |- ( ( ph -> ps ) -> ( ( ps -> ch ) -> ( ph -> ch ) ) )

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