Theorem merco1lem10 1491

Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 1478. (Contributed by Anthony Hart, 18-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
merco1lem10	|- (((((ph -> ps) -> ch) -> (ta -> ch)) -> ph) -> (th -> ph))

Proof of Theorem merco1lem10

Step	Hyp	Ref	Expression
1		merco1 1478	. . 3 |- (((((ch -> ph) -> (ta -> F. )) -> ph) -> (ph -> ps)) -> (((ph -> ps) -> ch) -> (ta -> ch)))
2		merco1lem2 1482	. . 3 |- ((((((ch -> ph) -> (ta -> F. )) -> ph) -> (ph -> ps)) -> (((ph -> ps) -> ch) -> (ta -> ch))) -> ((((ph -> ps) -> (th -> F. )) -> ((((ch -> ph) -> (ta -> F. )) -> ph) -> F. )) -> (((ph -> ps) -> ch) -> (ta -> ch))))
3	1, 2	ax-mp 5	. 2 |- ((((ph -> ps) -> (th -> F. )) -> ((((ch -> ph) -> (ta -> F. )) -> ph) -> F. )) -> (((ph -> ps) -> ch) -> (ta -> ch)))
4		merco1 1478	. 2 |- (((((ph -> ps) -> (th -> F. )) -> ((((ch -> ph) -> (ta -> F. )) -> ph) -> F. )) -> (((ph -> ps) -> ch) -> (ta -> ch))) -> (((((ph -> ps) -> ch) -> (ta -> ch)) -> ph) -> (th -> ph)))
5	3, 4	ax-mp 5	1 |- (((((ph -> ps) -> ch) -> (ta -> ch)) -> ph) -> (th -> ph))

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:  retbwax1  1500