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Metamath Proof Explorer

Theorem syl6d

Description: A nested syllogism deduction. Deduction associated with syl6 . (Contributed by NM, 11-May-1993) (Proof shortened by Josh Purinton, 29-Dec-2000) (Proof shortened by Mel L. O'Cat, 2-Feb-2006)

	Ref	Expression
Hypotheses	syl6d.1	$⊢ φ \to (ψ \to (χ \to θ))$
	syl6d.2	$⊢ φ \to (θ \to τ)$
Assertion	syl6d	$⊢ φ \to (ψ \to (χ \to τ))$

Proof

Step	Hyp	Ref	Expression
1		syl6d.1	$⊢ φ \to (ψ \to (χ \to θ))$
2		syl6d.2	$⊢ φ \to (θ \to τ)$
3	2	a1d	$⊢ φ \to (ψ \to (θ \to τ))$
4	1 3	syldd	$⊢ φ \to (ψ \to (χ \to τ))$