Metamath Proof Explorer

Theorem imim12d

Description: Deduction combining antecedents and consequents. Deduction associated with imim12 and imim12i . (Contributed by NM, 7-Aug-1994) (Proof shortened by Mel L. O'Cat, 30-Oct-2011)

	Ref	Expression
Hypotheses	imim12d.1	$⊢ φ \to (ψ \to χ)$
	imim12d.2	$⊢ φ \to (θ \to τ)$
Assertion	imim12d	$⊢ φ \to ((χ \to θ) \to (ψ \to τ))$

Proof

Step	Hyp	Ref	Expression
1		imim12d.1	$⊢ φ \to (ψ \to χ)$
2		imim12d.2	$⊢ φ \to (θ \to τ)$
3	2	imim2d	$⊢ φ \to ((χ \to θ) \to (χ \to τ))$
4	1 3	syl5d	$⊢ φ \to ((χ \to θ) \to (ψ \to τ))$