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Metamath Proof Explorer

Theorem pm2.86d

Description: Deduction associated with pm2.86 . (Contributed by NM, 29-Jun-1995) (Proof shortened by Wolf Lammen, 3-Apr-2013)

		Ref	Expression
	Hypothesis	pm2.86d.1	$⊢ φ \to ((ψ \to χ) \to (ψ \to θ))$
	Assertion	pm2.86d	$⊢ φ \to (ψ \to (χ \to θ))$

Step	Hyp	Ref	Expression
1		pm2.86d.1	$⊢ φ \to ((ψ \to χ) \to (ψ \to θ))$
2		ax-1	$⊢ χ \to (ψ \to χ)$
3	2 1	syl5	$⊢ φ \to (χ \to (ψ \to θ))$
4	3	com23	$⊢ φ \to (ψ \to (χ \to θ))$