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Metamath Proof Explorer

Theorem a1ddd

Description: Triple deduction introducing an antecedent to a wff. Deduction associated with a1dd . Double deduction associated with a1d . Triple deduction associated with ax-1 and a1i . (Contributed by Jeff Hankins, 4-Aug-2009)

		Ref	Expression
	Hypothesis	a1ddd.1	$⊢ φ \to (ψ \to (χ \to τ))$
	Assertion	a1ddd	$⊢ φ \to (ψ \to (χ \to (θ \to τ)))$

Proof

Step	Hyp	Ref	Expression
1		a1ddd.1	$⊢ φ \to (ψ \to (χ \to τ))$
2		ax-1	$⊢ τ \to (θ \to τ)$
3	1 2	syl8	$⊢ φ \to (ψ \to (χ \to (θ \to τ)))$