Theorem merco1lem7 1487

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
merco1lem7	|- (ph -> (((ps -> ch) -> ps) -> ps))

Proof of Theorem merco1lem7

Step	Hyp	Ref	Expression
1		merco1lem5 1485	. . 3 |- ((((ps -> F. ) -> (((ps -> ch) -> ps) -> F. )) -> ch) -> (ps -> ch))
2		merco1 1478	. . 3 |- (((((ps -> F. ) -> (((ps -> ch) -> ps) -> F. )) -> ch) -> (ps -> ch)) -> (((ps -> ch) -> ps) -> (((ps -> ch) -> ps) -> ps)))
3	1, 2	ax-mp 5	. 2 |- (((ps -> ch) -> ps) -> (((ps -> ch) -> ps) -> ps))
4		merco1lem6 1486	. 2 |- ((((ps -> ch) -> ps) -> (((ps -> ch) -> ps) -> ps)) -> (ph -> (((ps -> ch) -> ps) -> ps)))
5	3, 4	ax-mp 5	1 |- (ph -> (((ps -> ch) -> ps) -> ps))

Syntax hints:   -> wi 4   F. wfal 1317

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:  retbwax3  1488  merco1lem17  1498