Theorem luklem1 661

Description: Lemma for rederiving standard propositional axioms from Lukasiewicz'.

Hypotheses

Ref	Expression
luklem1.1	⊢ (φ → ψ)
luklem1.2	⊢ (ψ → χ)

Assertion

Ref	Expression
luklem1	⊢ (φ → χ)

Proof of Theorem luklem1

Step	Hyp	Ref	Expression
1		luklem1.2	. 2 ⊢ (ψ → χ)
2		luklem1.1	. . 3 ⊢ (φ → ψ)
3		luk-1 658	. . 3 ⊢ ((φ → ψ) → ((ψ → χ) → (φ → χ)))
4	2, 3	ax-mp 6	. 2 ⊢ ((ψ → χ) → (φ → χ))
5	1, 4	ax-mp 6	1 ⊢ (φ → χ)

Syntax hints:   → wi 2

This theorem is referenced by:  luklem2 662  luklem3 663  luklem4 664  luklem5 665  luklem6 666  luklem7 667  ax2 670  ax3 671

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

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