Theorem luklem1 1423

Description: Used to rederive standard propositional axioms from Lukasiewicz'. (Contributed by NM, 23-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)

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 1420	. . 3 ⊢ ((φ → ψ) → ((ψ → χ) → (φ → χ)))
4	2, 3	ax-mp 5	. 2 ⊢ ((ψ → χ) → (φ → χ))
5	1, 4	ax-mp 5	1 ⊢ (φ → χ)

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-meredith 1406

This theorem is referenced by:  luklem2  1424  luklem3  1425  luklem4  1426  luklem5  1427  luklem6  1428  luklem7  1429  ax2  1432  ax3  1433