Metamath Proof Explorer

Theorem imim12

Description: Closed form of imim12i and of 3syl . (Contributed by BJ, 16-Jul-2019)

		Ref	Expression
	Assertion	imim12	$⊢ (φ \to ψ) \to ((χ \to θ) \to ((ψ \to χ) \to (φ \to θ)))$

Step	Hyp	Ref	Expression
1		imim2	$⊢ (χ \to θ) \to ((ψ \to χ) \to (ψ \to θ))$
2		imim1	$⊢ (φ \to ψ) \to ((ψ \to θ) \to (φ \to θ))$
3	1 2	syl9r	$⊢ (φ \to ψ) \to ((χ \to θ) \to ((ψ \to χ) \to (φ \to θ)))$