Theorem merco1lem15 1656

Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 1638. (Contributed by Anthony Hart, 18-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
merco1lem15	|- ( ( ph -> ps ) -> ( ph -> ( ch -> ps ) ) )

Proof of Theorem merco1lem15

Step	Hyp	Ref	Expression
1		merco1lem14 1655	. 2 |- ( ( ( ( ph -> ps ) -> ps ) -> ( ch -> ps ) ) -> ( ph -> ( ch -> ps ) ) )
2		merco1lem13 1654	. 2 |- ( ( ( ( ( ph -> ps ) -> ps ) -> ( ch -> ps ) ) -> ( ph -> ( ch -> ps ) ) ) -> ( ( ph -> ps ) -> ( ph -> ( ch -> ps ) ) ) )
3	1, 2	ax-mp 5	1 |- ( ( ph -> ps ) -> ( ph -> ( ch -> ps ) ) )

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:  merco1lem16  1657  retbwax1  1660