Theorem syldd 61

Description: Nested syllogism deduction. (Contributed by NM, 12-Dec-2004.) (Proof shortened by Wolf Lammen, 11-May-2013.)

Hypotheses

Ref	Expression
syldd.1	⊢ (φ → (ψ → (χ → θ)))
syldd.2	⊢ (φ → (ψ → (θ → τ)))

Assertion

Ref	Expression
syldd	⊢ (φ → (ψ → (χ → τ)))

Proof of Theorem syldd

Step	Hyp	Ref	Expression
1		syldd.2	. 2 ⊢ (φ → (ψ → (θ → τ)))
2		syldd.1	. 2 ⊢ (φ → (ψ → (χ → θ)))
3		imim2 49	. 2 ⊢ ((θ → τ) → ((χ → θ) → (χ → τ)))
4	1, 2, 3	syl6c 60	1 ⊢ (φ → (ψ → (χ → τ)))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is used by:  syl5d  62  syl6d  64  ee23  1364