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Theorem dcbiit 824
Description: Equivalence property for decidability. Closed form. (Contributed by BJ, 27-Jan-2020.)
Assertion
Ref Expression
dcbiit ((𝜑𝜓) → (DECID 𝜑DECID 𝜓))

Proof of Theorem dcbiit
StepHypRef Expression
1 id 19 . 2 ((𝜑𝜓) → (𝜑𝜓))
21dcbid 823 1 ((𝜑𝜓) → (DECID 𝜑DECID 𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 104  DECID wdc 819
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-in1 603  ax-in2 604  ax-io 698
This theorem depends on definitions:  df-bi 116  df-dc 820
This theorem is referenced by:  dcbii  825  bj-d0clsepcl  13137
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