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Metamath Proof Explorer

Theorem pm2.43d

Description: Deduction absorbing redundant antecedent. Deduction associated with pm2.43 and pm2.43i . (Contributed by NM, 18-Aug-1993) (Proof shortened by Mel L. O'Cat, 28-Nov-2008)

		Ref	Expression
	Hypothesis	pm2.43d.1	$⊢ φ \to (ψ \to (ψ \to χ))$
	Assertion	pm2.43d	$⊢ φ \to (ψ \to χ)$

Proof

Step	Hyp	Ref	Expression
1		pm2.43d.1	$⊢ φ \to (ψ \to (ψ \to χ))$
2		id	$⊢ ψ \to ψ$
3	2 1	mpdi	$⊢ φ \to (ψ \to χ)$