Theorem merlem4 1410

Description: Step 8 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
merlem4	|- (ta -> ((ta -> ph) -> (th -> ph)))

Proof of Theorem merlem4

Step	Hyp	Ref	Expression
1		ax-meredith 1406	. 2 |- (((((ph -> ph) -> (-. th -> -. th)) -> th) -> ta) -> ((ta -> ph) -> (th -> ph)))
2		merlem3 1409	. 2 |- ((((((ph -> ph) -> (-. th -> -. th)) -> th) -> ta) -> ((ta -> ph) -> (th -> ph))) -> (ta -> ((ta -> ph) -> (th -> ph))))
3	1, 2	ax-mp 5	1 |- (ta -> ((ta -> ph) -> (th -> ph)))

Syntax hints:  -. wn 3   -> wi 4

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

This theorem is referenced by:  merlem5  1411  merlem6  1412  merlem7  1413  merlem12  1418  luk-2  1421