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Theorem orsild 32842
Description: A lemma for not-or-not elimination, in deduction form. (Contributed by Giovanni Mascellani, 15-Sep-2017.)
Hypothesis
Ref Expression
orsild.1 (𝜑 → ¬ (𝜓𝜒))
Assertion
Ref Expression
orsild (𝜑 → ¬ 𝜓)

Proof of Theorem orsild
StepHypRef Expression
1 orsild.1 . . 3 (𝜑 → ¬ (𝜓𝜒))
2 ioran 509 . . 3 (¬ (𝜓𝜒) ↔ (¬ 𝜓 ∧ ¬ 𝜒))
31, 2sylib 206 . 2 (𝜑 → (¬ 𝜓 ∧ ¬ 𝜒))
43simpld 473 1 (𝜑 → ¬ 𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 381  wa 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 195  df-or 383  df-an 384
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator