Theorem syl6d 54

Description: A nested syllogism deduction. (The proof was shortened by Josh Purinton, 29-Dec-00.)

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	syl3d 26	. 2 ⊢ (φ → ((χ → θ) → (χ → τ)))
4	1, 3	syld 27	1 ⊢ (φ → (ψ → (χ → τ)))

Syntax hints:   → wi 2

This theorem is referenced by:  cbv1 845  sbi1 884  tfinds 2401  ltexprlem7 3942

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

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