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Theorem imorr 711
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 883. (Contributed by Jim Kingdon, 21-Jul-2018.)
Assertion
Ref Expression
imorr ((¬ 𝜑𝜓) → (𝜑𝜓))

Proof of Theorem imorr
StepHypRef Expression
1 ax-in2 605 . 2 𝜑 → (𝜑𝜓))
2 ax-1 6 . 2 (𝜓 → (𝜑𝜓))
31, 2jaoi 706 1 ((¬ 𝜑𝜓) → (𝜑𝜓))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wo 698
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 605  ax-io 699
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  pm4.52im  740  nf4r  1650
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