Theorem merco1lem4 1484

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
merco1lem4	|- (((ph -> ps) -> ch) -> (ps -> ch))

Proof of Theorem merco1lem4

Step	Hyp	Ref	Expression
1		merco1lem3 1483	. . 3 |- ((((ps -> F. ) -> (ph -> F. )) -> ((ch -> ph) -> F. )) -> ((ch -> ph) -> (ps -> F. )))
2		merco1 1478	. . 3 |- (((((ps -> F. ) -> (ph -> F. )) -> ((ch -> ph) -> F. )) -> ((ch -> ph) -> (ps -> F. ))) -> ((((ch -> ph) -> (ps -> F. )) -> ps) -> (ph -> ps)))
3	1, 2	ax-mp 5	. 2 |- ((((ch -> ph) -> (ps -> F. )) -> ps) -> (ph -> ps))
4		merco1 1478	. 2 |- (((((ch -> ph) -> (ps -> F. )) -> ps) -> (ph -> ps)) -> (((ph -> ps) -> ch) -> (ps -> ch)))
5	3, 4	ax-mp 5	1 |- (((ph -> ps) -> ch) -> (ps -> ch))

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:  merco1lem5  1485  merco1lem11  1492  merco1lem13  1494  merco1lem17  1498  merco1lem18  1499