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	⊢ (φ → (¬ φ → ψ))

Proof of Theorem luk-3

Step	Hyp	Ref	Expression
1		merlem11 1417	. 2 ⊢ ((¬ φ → (¬ φ → ψ)) → (¬ φ → ψ))
2		merlem1 1407	. 2 ⊢ (((¬ φ → (¬ φ → ψ)) → (¬ φ → ψ)) → (φ → (¬ φ → ψ)))
3	1, 2	ax-mp 5	1 ⊢ (φ → (¬ φ → ψ))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4

This proof depends on axioms:  ax-mp 5  ax-meredith 1406

This theorem is used by:  luklem2  1424  luklem3  1425