Theorem merlem11 1417

Description: Step 20 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
merlem11	|- ((ph -> (ph -> ps)) -> (ph -> ps))

Proof of Theorem merlem11

Step	Hyp	Ref	Expression
1		ax-meredith 1406	. 2 |- (((((ph -> ph) -> (-. ph -> -. ph)) -> ph) -> ph) -> ((ph -> ph) -> (ph -> ph)))
2		merlem10 1416	. . 3 |- ((ph -> (ph -> ps)) -> ((ph -> (ph -> ps)) -> (ph -> ps)))
3		merlem10 1416	. . 3 |- (((ph -> (ph -> ps)) -> ((ph -> (ph -> ps)) -> (ph -> ps))) -> ((((((ph -> ph) -> (-. ph -> -. ph)) -> ph) -> ph) -> ((ph -> ph) -> (ph -> ph))) -> ((ph -> (ph -> ps)) -> (ph -> ps))))
4	2, 3	ax-mp 5	. 2 |- ((((((ph -> ph) -> (-. ph -> -. ph)) -> ph) -> ph) -> ((ph -> ph) -> (ph -> ph))) -> ((ph -> (ph -> ps)) -> (ph -> ps)))
5	1, 4	ax-mp 5	1 |- ((ph -> (ph -> ps)) -> (ph -> ps))

Syntax hints:  -. wn 3   -> wi 4

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

This theorem is referenced by:  merlem12  1418  merlem13  1419  luk-2  1421  luk-3  1422