Theorem luklem5 1427

Description: Used to rederive standard propositional axioms from Lukasiewicz'. (Contributed by NM, 22-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
luklem5	⊢ (φ → (ψ → φ))

Proof of Theorem luklem5

Step	Hyp	Ref	Expression
1		luklem3 1425	. 2 ⊢ (φ → (((¬ φ → φ) → φ) → (ψ → φ)))
2		luklem4 1426	. 2 ⊢ ((((¬ φ → φ) → φ) → (ψ → φ)) → (ψ → φ))
3	1, 2	luklem1 1423	1 ⊢ (φ → (ψ → φ))

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:  luklem6  1428  luklem7  1429  ax1  1431