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Metamath Proof Explorer

Theorem 3impd

Description: Importation deduction for triple conjunction. (Contributed by NM, 26-Oct-2006)

		Ref	Expression
	Hypothesis	3imp1.1	$⊢ φ \to (ψ \to (χ \to (θ \to τ)))$
	Assertion	3impd	$⊢ φ \to ((ψ \land χ \land θ) \to τ)$

Step	Hyp	Ref	Expression
1		3imp1.1	$⊢ φ \to (ψ \to (χ \to (θ \to τ)))$
2	1	com4l	$⊢ ψ \to (χ \to (θ \to (φ \to τ)))$
3	2	3imp	$⊢ (ψ \land χ \land θ) \to (φ \to τ)$
4	3	com12	$⊢ φ \to ((ψ \land χ \land θ) \to τ)$