Theorem merlem6 1647

Description: Step 12 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
merlem6	⊢ (𝜒 → (((𝜓 → 𝜒) → 𝜑) → (𝜃 → 𝜑)))

Proof of Theorem merlem6

Step	Hyp	Ref	Expression
1		merlem4 1645	. 2 ⊢ ((𝜓 → 𝜒) → (((𝜓 → 𝜒) → 𝜑) → (𝜃 → 𝜑)))
2		merlem3 1644	. 2 ⊢ (((𝜓 → 𝜒) → (((𝜓 → 𝜒) → 𝜑) → (𝜃 → 𝜑))) → (𝜒 → (((𝜓 → 𝜒) → 𝜑) → (𝜃 → 𝜑))))
3	1, 2	ax-mp 5	1 ⊢ (𝜒 → (((𝜓 → 𝜒) → 𝜑) → (𝜃 → 𝜑)))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by:  merlem7  1648  merlem9  1650  merlem13  1654