Theorem merlem6 650

Description: Step 12 of Meredith's proof of Lukasiewicz axioms from his sole axiom.

Assertion

Ref	Expression
merlem6	⊢ (χ → (((ψ → χ) → φ) → (θ → φ)))

Proof of Theorem merlem6

Step	Hyp	Ref	Expression
1		merlem4 648	. 2 ⊢ ((ψ → χ) → (((ψ → χ) → φ) → (θ → φ)))
2		merlem3 647	. 2 ⊢ (((ψ → χ) → (((ψ → χ) → φ) → (θ → φ))) → (χ → (((ψ → χ) → φ) → (θ → φ))))
3	1, 2	ax-mp 6	1 ⊢ (χ → (((ψ → χ) → φ) → (θ → φ)))

Syntax hints:   → wi 2

This theorem is referenced by:  merlem7 651  merlem9 653  merlem13 657

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

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