Theorem pm2.61d

Description: Deduction eliminating an antecedent. (Contributed by NM, 27-Apr-1994) (Proof shortened by Wolf Lammen, 12-Sep-2013)

	Ref	Expression
Hypotheses	pm2.61d.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
	pm2.61d.2	$$⊢\phi \to \left(\neg \psi \to \chi \right)$$
Assertion	pm2.61d	$$⊢\phi \to \chi$$

Proof

Step	Hyp	Ref	Expression
1		pm2.61d.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		pm2.61d.2	$$⊢\phi \to \left(\neg \psi \to \chi \right)$$
3	2	con1d	$$⊢\phi \to \left(\neg \chi \to \psi \right)$$
4	3 1	syld	$$⊢\phi \to \left(\neg \chi \to \chi \right)$$
5	4	pm2.18d	$$⊢\phi \to \chi$$