Theorem syl6d 64

Description: A nested syllogism deduction. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Josh Purinton, 29-Dec-2000.) (Proof shortened by O'Cat, 2-Feb-2006.)

Hypotheses

Ref	Expression
syl6d.1	⊢ (φ → (ψ → (χ → θ)))
syl6d.2	⊢ (φ → (θ → τ))

Assertion

Ref	Expression
syl6d	⊢ (φ → (ψ → (χ → τ)))

Proof of Theorem syl6d

Step	Hyp	Ref	Expression
1		syl6d.1	. 2 ⊢ (φ → (ψ → (χ → θ)))
2		syl6d.2	. . 3 ⊢ (φ → (θ → τ))
3	2	a1d 22	. 2 ⊢ (φ → (ψ → (θ → τ)))
4	1, 3	syldd 61	1 ⊢ (φ → (ψ → (χ → τ)))

Syntax hints:   → wi 4

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

This theorem is referenced by:  syl8  65  cbv1h  1978  sbi1  2063