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Metamath Proof Explorer

Theorem pm2.83

Description: Theorem *2.83 of WhiteheadRussell p. 108. Closed form of syld . (Contributed by NM, 3-Jan-2005)

		Ref	Expression
	Assertion	pm2.83	$⊢ (φ \to (ψ \to χ)) \to ((φ \to (χ \to θ)) \to (φ \to (ψ \to θ)))$

Step	Hyp	Ref	Expression
1		imim1	$⊢ (ψ \to χ) \to ((χ \to θ) \to (ψ \to θ))$
2	1	imim3i	$⊢ (φ \to (ψ \to χ)) \to ((φ \to (χ \to θ)) \to (φ \to (ψ \to θ)))$