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Theorem dcbii 826
Description: Equivalence property for decidability. Inference form. (Contributed by Jim Kingdon, 28-Mar-2018.)
Hypothesis
Ref Expression
dcbii.1 (𝜑𝜓)
Assertion
Ref Expression
dcbii (DECID 𝜑DECID 𝜓)

Proof of Theorem dcbii
StepHypRef Expression
1 dcbii.1 . 2 (𝜑𝜓)
2 dcbiit 825 . 2 ((𝜑𝜓) → (DECID 𝜑DECID 𝜓))
31, 2ax-mp 5 1 (DECID 𝜑DECID 𝜓)
Colors of variables: wff set class
Syntax hints:  wb 104  DECID wdc 820
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 604  ax-in2 605  ax-io 699
This theorem depends on definitions:  df-bi 116  df-dc 821
This theorem is referenced by:  dcbi  921  dcned  2333  dfrex2dc  2448  euxfr2dc  2897  exmidexmid  4158  pw1fin  6856  dcfi  6926  exfzdc  10143  fprod1p  11500  prmdc  12011  nninfdclemcl  12221  nninfdclemp1  12223  nninfsellemdc  13624
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