Theorem re1tbw2 1511

Description: tbw-ax2 1466 rederived from merco2 1501. (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 1502	. . . 4 |- (((ph -> ph) -> ph) -> (ph -> (ps -> ph)))
2		mercolem1 1502	. . . 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 1507	. . 3 |- ((ph -> (ps -> (ph -> (ps -> ph)))) -> (ps -> (ph -> (ps -> ph))))
5	3, 4	ax-mp 5	. 2 |- (ps -> (ph -> (ps -> ph)))
6		mercolem6 1507	. 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 177  df-tru 1319  df-fal 1320

This theorem is referenced by:  re1tbw4  1513