Theorem notornotel2 33068

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

Hypothesis

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

Assertion

Ref	Expression
notornotel2	⊢ (𝜑 → 𝜒)

Proof of Theorem notornotel2

Step	Hyp	Ref	Expression
1		notornotel2.1	. . 3 ⊢ (𝜑 → ¬ (𝜓 ∨ ¬ 𝜒))
2		orcom 401	. . 3 ⊢ ((¬ 𝜒 ∨ 𝜓) ↔ (𝜓 ∨ ¬ 𝜒))
3	1, 2	sylnibr 318	. 2 ⊢ (𝜑 → ¬ (¬ 𝜒 ∨ 𝜓))
4	3	notornotel1 33067	1 ⊢ (𝜑 → 𝜒)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 382

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385

This theorem is referenced by:  ac6s6  33150