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Theorem notornotel1 35526
Description: A lemma for not-or-not elimination, in deduction form. (Contributed by Giovanni Mascellani, 19-Mar-2018.)
Hypothesis
Ref Expression
notornotel1.1 (𝜑 → ¬ (¬ 𝜓𝜒))
Assertion
Ref Expression
notornotel1 (𝜑𝜓)

Proof of Theorem notornotel1
StepHypRef Expression
1 notornotel1.1 . 2 (𝜑 → ¬ (¬ 𝜓𝜒))
2 ioran 981 . . . 4 (¬ (¬ 𝜓𝜒) ↔ (¬ ¬ 𝜓 ∧ ¬ 𝜒))
32biimpi 219 . . 3 (¬ (¬ 𝜓𝜒) → (¬ ¬ 𝜓 ∧ ¬ 𝜒))
4 simpl 486 . . 3 ((¬ ¬ 𝜓 ∧ ¬ 𝜒) → ¬ ¬ 𝜓)
5 notnotr 132 . . 3 (¬ ¬ 𝜓𝜓)
63, 4, 53syl 18 . 2 (¬ (¬ 𝜓𝜒) → 𝜓)
71, 6syl 17 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wa 399  wo 844
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 210  df-an 400  df-or 845
This theorem is referenced by:  notornotel2  35527  ac6s6  35603
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