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Theorem imorr 785
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 784. (Contributed by Jim Kingdon, 21-Jul-2018.)
Assertion
Ref Expression
imorr ((¬ φ ψ) → (φψ))

Proof of Theorem imorr
StepHypRef Expression
1 ax-in2 533 . 2 φ → (φψ))
2 ax-1 5 . 2 (ψ → (φψ))
31, 2jaoi 623 1 ((¬ φ ψ) → (φψ))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   wo 616
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in2 533  ax-io 617
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  pm4.52im  791  nf4r  1539
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