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Metamath Proof Explorer

Theorem pm2.86

Description: Converse of Axiom ax-2 . Theorem *2.86 of WhiteheadRussell p. 108. (Contributed by NM, 25-Apr-1994) (Proof shortened by Wolf Lammen, 3-Apr-2013)

		Ref	Expression
	Assertion	pm2.86	$⊢ ((φ \to ψ) \to (φ \to χ)) \to (φ \to (ψ \to χ))$

Proof

Step	Hyp	Ref	Expression
1		id	$⊢ ((φ \to ψ) \to (φ \to χ)) \to ((φ \to ψ) \to (φ \to χ))$
2	1	pm2.86d	$⊢ ((φ \to ψ) \to (φ \to χ)) \to (φ \to (ψ \to χ))$