Theorem re1tbw1 1510

Description: tbw-ax1 1465 rederived from merco2 1501. (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 1509	. . 3 |- ((ph -> ps) -> ((ps -> (ph -> ch)) -> ((ph -> ps) -> ((ps -> ch) -> (ph -> ch)))))
2		mercolem3 1504	. . 3 |- ((ps -> ch) -> (ps -> (ph -> ch)))
3		mercolem6 1507	. . 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 59	. 2 |- ((ps -> ch) -> ((ph -> ps) -> ((ps -> ch) -> (ph -> ch))))
5		mercolem6 1507	. 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 177  df-tru 1319  df-fal 1320

This theorem is referenced by:  re1tbw4  1513