Theorem merlem2 1408

Description: Step 4 of Meredith's proof of Lukasiewicz axioms from his sole axiom. (Contributed by NM, 14-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
merlem2	|- (((ph -> ph) -> ch) -> (th -> ch))

Proof of Theorem merlem2

Step	Hyp	Ref	Expression
1		merlem1 1407	. 2 |- ((((ch -> ch) -> (-. ph -> -. th)) -> ph) -> (ph -> ph))
2		ax-meredith 1406	. 2 |- (((((ch -> ch) -> (-. ph -> -. th)) -> ph) -> (ph -> ph)) -> (((ph -> ph) -> ch) -> (th -> ch)))
3	1, 2	ax-mp 5	1 |- (((ph -> ph) -> ch) -> (th -> ch))

Syntax hints:  -. wn 3   -> wi 4

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

This theorem is referenced by:  merlem3  1409  merlem12  1418