Theorem syl5d 62

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
syl5d.1	⊢ (φ → (ψ → χ))
syl5d.2	⊢ (φ → (θ → (χ → τ)))

Assertion

Ref	Expression
syl5d	⊢ (φ → (θ → (ψ → τ)))

Proof of Theorem syl5d

Step	Hyp	Ref	Expression
1		syl5d.1	. . 3 ⊢ (φ → (ψ → χ))
2	1	a1d 22	. 2 ⊢ (φ → (θ → (ψ → χ)))
3		syl5d.2	. 2 ⊢ (φ → (θ → (χ → τ)))
4	2, 3	syldd 61	1 ⊢ (φ → (θ → (ψ → 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:  syl7  63  syl9  66  imim12d  68  sbi1  2063