Theorem luk-3 937

Description: 3 of 3 axioms for propositional calculus due to Lukasiewicz, derived from Meredith's sole axiom.

Assertion

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

Proof of Theorem luk-3

Step	Hyp	Ref	Expression
1		merlem11 932	. 2 |- ((-. ph -> (-. ph -> ps)) -> (-. ph -> ps))
2		merlem1 922	. 2 |- (((-. ph -> (-. ph -> ps)) -> (-. ph -> ps)) -> (ph -> (-. ph -> ps)))
3	1, 2	ax-mp 7	1 |- (ph -> (-. ph -> ps))

Syntax hints:  -. wn 2   -> wi 3

This theorem is referenced by:  luklem2 939  luklem3 940

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

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