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Metamath Proof Explorer

Theorem expt

Description: Exportation theorem pm3.3 (closed form of ex ) expressed with primitive connectives. (Contributed by NM, 28-Dec-1992)

		Ref	Expression
	Assertion	expt	$⊢ (\neg (φ \to \neg ψ) \to χ) \to (φ \to (ψ \to χ))$

Step	Hyp	Ref	Expression
1		pm3.2im	$⊢ φ \to (ψ \to \neg (φ \to \neg ψ))$
2	1	imim1d	$⊢ φ \to ((\neg (φ \to \neg ψ) \to χ) \to (ψ \to χ))$
3	2	com12	$⊢ (\neg (φ \to \neg ψ) \to χ) \to (φ \to (ψ \to χ))$