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Theorem dcbiit 839
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 838 1 ((𝜑𝜓) → (DECID 𝜑DECID 𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 105  DECID wdc 834
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-io 709
This theorem depends on definitions:  df-bi 117  df-dc 835
This theorem is referenced by:  dcbii  840  bj-d0clsepcl  14326
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