Theorem luk-3 1422

Description: 3 of 3 axioms for propositional calculus due to Lukasiewicz, derived from Meredith's sole axiom. (Contributed by NM, 14-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
luk-3	|- (ph -> (-. ph -> ps))

Proof of Theorem luk-3

Step	Hyp	Ref	Expression
1		merlem11 1417	. 2 |- ((-. ph -> (-. ph -> ps)) -> (-. ph -> ps))
2		merlem1 1407	. 2 |- (((-. ph -> (-. ph -> ps)) -> (-. ph -> ps)) -> (ph -> (-. ph -> ps)))
3	1, 2	ax-mp 5	1 |- (ph -> (-. 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:  luklem2  1424  luklem3  1425