Theorem merco1lem9 1650

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
merco1lem9	|- ( ( ph -> ( ph -> ps ) ) -> ( ph -> ps ) )

Proof of Theorem merco1lem9

Step	Hyp	Ref	Expression
1		merco1lem8 1649	. 2 |- ( ( F. -> ph ) -> ( ( ph -> ( ph -> ps ) ) -> ( ph -> ps ) ) )
2		merco1lem8 1649	. 2 |- ( ( ( F. -> ph ) -> ( ( ph -> ( ph -> ps ) ) -> ( ph -> ps ) ) ) -> ( ( ph -> ( ph -> ps ) ) -> ( ph -> ps ) ) )
3	1, 2	ax-mp 5	1 |- ( ( ph -> ( ph -> ps ) ) -> ( ph -> ps ) )

Syntax hints:   -> wi 4   F. wfal 1488

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:  merco1lem12  1653  merco1lem14  1655  merco1lem17  1658  merco1lem18  1659  retbwax1  1660