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Theorem pm5.13dc 882
Description: An implication holds in at least one direction, where one proposition is decidable. Based on theorem *5.13 of [WhiteheadRussell] p. 123. (Contributed by Jim Kingdon, 30-Mar-2018.)
Assertion
Ref Expression
pm5.13dc (DECID 𝜓 → ((𝜑𝜓) ∨ (𝜓𝜑)))

Proof of Theorem pm5.13dc
StepHypRef Expression
1 pm5.14dc 881 1 (DECID 𝜓 → ((𝜑𝜓) ∨ (𝜓𝜑)))
Colors of variables: wff set class
Syntax hints:  wi 4  wo 682  DECID wdc 804
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 589  ax-io 683
This theorem depends on definitions:  df-bi 116  df-dc 805
This theorem is referenced by: (None)
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