Theorem merco1lem8 1489

Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 1478. (Contributed by Anthony Hart, 17-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
merco1lem8	|- (ph -> ((ps -> (ps -> ch)) -> (ps -> ch)))

Proof of Theorem merco1lem8

Step	Hyp	Ref	Expression
1		merco1lem6 1486	. 2 |- ((ps -> (ps -> ch)) -> ((ps -> (ps -> ch)) -> (ps -> ch)))
2		merco1lem6 1486	. 2 |- (((ps -> (ps -> ch)) -> ((ps -> (ps -> ch)) -> (ps -> ch))) -> (ph -> ((ps -> (ps -> ch)) -> (ps -> ch))))
3	1, 2	ax-mp 5	1 |- (ph -> ((ps -> (ps -> ch)) -> (ps -> 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:  merco1lem9  1490  merco1lem14  1495