Theorem merlem8 1414

Description: Step 15 of Meredith's proof of Lukasiewicz axioms from his sole axiom. (Contributed by NM, 22-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
merlem8	|- (((ps -> ch) -> th) -> (((ch -> ta) -> (-. th -> -. ps)) -> th))

Proof of Theorem merlem8

Step	Hyp	Ref	Expression
1		ax-meredith 1406	. 2 |- (((((ph -> ph) -> (-. ph -> -. ph)) -> ph) -> ph) -> ((ph -> ph) -> (ph -> ph)))
2		merlem7 1413	. 2 |- ((((((ph -> ph) -> (-. ph -> -. ph)) -> ph) -> ph) -> ((ph -> ph) -> (ph -> ph))) -> (((ps -> ch) -> th) -> (((ch -> ta) -> (-. th -> -. ps)) -> th)))
3	1, 2	ax-mp 5	1 |- (((ps -> ch) -> th) -> (((ch -> ta) -> (-. th -> -. ps)) -> th))

Syntax hints:  -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-meredith 1406

This theorem is referenced by:  merlem9  1415