Metamath Proof Explorer

Theorem imdi

Description: Distributive law for implication. Compare Theorem *5.41 of WhiteheadRussell p. 125. (Contributed by NM, 5-Aug-1993)

		Ref	Expression
	Assertion	imdi	$⊢ (φ \to (ψ \to χ)) \leftrightarrow ((φ \to ψ) \to (φ \to χ))$

Step	Hyp	Ref	Expression
1		ax-2	$⊢ (φ \to (ψ \to χ)) \to ((φ \to ψ) \to (φ \to χ))$
2		pm2.86	$⊢ ((φ \to ψ) \to (φ \to χ)) \to (φ \to (ψ \to χ))$
3	1 2	impbii	$⊢ (φ \to (ψ \to χ)) \leftrightarrow ((φ \to ψ) \to (φ \to χ))$