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Theorem notornotel2 32851
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 (𝜑𝜒)

Proof of Theorem notornotel2
StepHypRef Expression
1 notornotel2.1 . . 3 (𝜑 → ¬ (𝜓 ∨ ¬ 𝜒))
2 orcom 400 . . 3 ((¬ 𝜒𝜓) ↔ (𝜓 ∨ ¬ 𝜒))
31, 2sylnibr 317 . 2 (𝜑 → ¬ (¬ 𝜒𝜓))
43notornotel1 32850 1 (𝜑𝜒)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 381
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 195  df-or 383  df-an 384
This theorem is referenced by:  ac6s6  32933
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