Theorem pm2.61nii

Description: Inference eliminating two antecedents. (Contributed by NM, 13-Jul-2005) (Proof shortened by Andrew Salmon, 25-May-2011) (Proof shortened by Wolf Lammen, 13-Nov-2012)

	Ref	Expression
Hypotheses	pm2.61nii.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
	pm2.61nii.2	$$⊢\neg \phi \to \chi$$
	pm2.61nii.3	$$⊢\neg \psi \to \chi$$
Assertion	pm2.61nii	$$⊢\chi$$

Proof

Step	Hyp	Ref	Expression
1		pm2.61nii.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		pm2.61nii.2	$$⊢\neg \phi \to \chi$$
3		pm2.61nii.3	$$⊢\neg \psi \to \chi$$
4	1 3	pm2.61d1	$$⊢\phi \to \chi$$
5	4 2	pm2.61i	$$⊢\chi$$