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	$$⊢\phi \to \left(\psi \to \left(\psi \to \chi \right)\right)$$
Assertion	pm2.43d	$$⊢\phi \to \left(\psi \to \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		pm2.43d.1	$$⊢\phi \to \left(\psi \to \left(\psi \to \chi \right)\right)$$
2		id	$$⊢\psi \to \psi$$
3	2 1	mpdi	$$⊢\phi \to \left(\psi \to \chi \right)$$