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Theorem dcbi 878
 Description: An equivalence of two decidable propositions is decidable. (Contributed by Jim Kingdon, 12-Apr-2018.)
Assertion
Ref Expression
dcbi DECID DECID DECID

Proof of Theorem dcbi
StepHypRef Expression
1 dcim 818 . . 3 DECID DECID DECID
2 dcim 818 . . . 4 DECID DECID DECID
32com12 30 . . 3 DECID DECID DECID
4 dcan 876 . . 3 DECID DECID DECID
51, 3, 4syl6c 65 . 2 DECID DECID DECID
6 dfbi2 380 . . 3
76dcbii 781 . 2 DECID DECID
85, 7syl6ibr 160 1 DECID DECID DECID
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103  DECID wdc 776 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663 This theorem depends on definitions:  df-bi 115  df-dc 777 This theorem is referenced by:  xor3dc  1319  pm5.15dc  1321  bilukdc  1328  xordidc  1331
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