Theorem merco1lem8 1649

Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 1638. (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 1646	. 2 |- ( ( ps -> ( ps -> ch ) ) -> ( ( ps -> ( ps -> ch ) ) -> ( ps -> ch ) ) )
2		merco1lem6 1646	. 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 197  df-tru 1486  df-fal 1489

This theorem is referenced by:  merco1lem9  1650  merco1lem14  1655