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Metamath Proof Explorer

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	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
	pm2.61nii.2	⊢ ( ¬ 𝜑 → 𝜒 )
	pm2.61nii.3	⊢ ( ¬ 𝜓 → 𝜒 )
Assertion	pm2.61nii	⊢ 𝜒

Proof

Step	Hyp	Ref	Expression
1		pm2.61nii.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		pm2.61nii.2	⊢ ( ¬ 𝜑 → 𝜒 )
3		pm2.61nii.3	⊢ ( ¬ 𝜓 → 𝜒 )
4	1 3	pm2.61d1	⊢ ( 𝜑 → 𝜒 )
5	4 2	pm2.61i	⊢ 𝜒