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Theorem imorr 831
Description: Implication in terms of disjunction. One direction of theorem *4.6 of [WhiteheadRussell] p. 120. The converse holds for decidable propositions, as seen at imordc 830. (Contributed by Jim Kingdon, 21-Jul-2018.)
Assertion
Ref Expression
imorr ((¬ 𝜑𝜓) → (𝜑𝜓))

Proof of Theorem imorr
StepHypRef Expression
1 ax-in2 578 . 2 𝜑 → (𝜑𝜓))
2 ax-1 5 . 2 (𝜓 → (𝜑𝜓))
31, 2jaoi 669 1 ((¬ 𝜑𝜓) → (𝜑𝜓))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wo 662
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-in2 578  ax-io 663
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  pm4.52im  837  nf4r  1602
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