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Metamath Proof Explorer

Theorem syl5d

Description: A nested syllogism deduction. Deduction associated with syl5 . (Contributed by NM, 14-May-1993) (Proof shortened by Josh Purinton, 29-Dec-2000) (Proof shortened by Mel L. O'Cat, 2-Feb-2006)

	Ref	Expression
Hypotheses	syl5d.1	$⊢ φ \to (ψ \to χ)$
	syl5d.2	$⊢ φ \to (θ \to (χ \to τ))$
Assertion	syl5d	$⊢ φ \to (θ \to (ψ \to τ))$

Proof

Step	Hyp	Ref	Expression
1		syl5d.1	$⊢ φ \to (ψ \to χ)$
2		syl5d.2	$⊢ φ \to (θ \to (χ \to τ))$
3	1	a1d	$⊢ φ \to (θ \to (ψ \to χ))$
4	3 2	syldd	$⊢ φ \to (θ \to (ψ \to τ))$