Theorem orsird

Description: A lemma for not-or-not elimination, in deduction form. (Contributed by Giovanni Mascellani, 15-Sep-2017)

	Ref	Expression
Hypothesis	orsild.1	⊢ ( 𝜑 → ¬ ( 𝜓 ∨ 𝜒 ) )
Assertion	orsird	⊢ ( 𝜑 → ¬ 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		orsild.1	⊢ ( 𝜑 → ¬ ( 𝜓 ∨ 𝜒 ) )
2		ioran	⊢ ( ¬ ( 𝜓 ∨ 𝜒 ) ↔ ( ¬ 𝜓 ∧ ¬ 𝜒 ) )
3	1 2	sylib	⊢ ( 𝜑 → ( ¬ 𝜓 ∧ ¬ 𝜒 ) )
4	3	simprd	⊢ ( 𝜑 → ¬ 𝜒 )