Theorem notornotel2

Description: A lemma for not-or-not elimination, in deduction form. (Contributed by Giovanni Mascellani, 19-Mar-2018)

	Ref	Expression
Hypothesis	notornotel2.1	⊢ ( 𝜑 → ¬ ( 𝜓 ∨ ¬ 𝜒 ) )
Assertion	notornotel2	⊢ ( 𝜑 → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		notornotel2.1	⊢ ( 𝜑 → ¬ ( 𝜓 ∨ ¬ 𝜒 ) )
2		orcom	⊢ ( ( ¬ 𝜒 ∨ 𝜓 ) ↔ ( 𝜓 ∨ ¬ 𝜒 ) )
3	1 2	sylnibr	⊢ ( 𝜑 → ¬ ( ¬ 𝜒 ∨ 𝜓 ) )
4	3	notornotel1	⊢ ( 𝜑 → 𝜒 )