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Theorem pm3.1 706
Description: Theorem *3.1 of [WhiteheadRussell] p. 111. The converse holds for decidable propositions, as seen at anordc 902. (Contributed by NM, 3-Jan-2005.) (Revised by Mario Carneiro, 31-Jan-2015.)
Assertion
Ref Expression
pm3.1 ((𝜑𝜓) → ¬ (¬ 𝜑 ∨ ¬ 𝜓))

Proof of Theorem pm3.1
StepHypRef Expression
1 pm3.14 705 . 2 ((¬ 𝜑 ∨ ¬ 𝜓) → ¬ (𝜑𝜓))
21con2i 592 1 ((𝜑𝜓) → ¬ (¬ 𝜑 ∨ ¬ 𝜓))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wa 102  wo 664
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-io 665
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  inssun  3239
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