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Theorem dcor 842
Description: A disjunction of two decidable propositions is decidable. (Contributed by Jim Kingdon, 21-Apr-2018.)
Assertion
Ref Expression
dcor DECID DECID DECID

Proof of Theorem dcor
StepHypRef Expression
1 df-dc 742 . 2 DECID
2 orc 632 . . . . . 6
32orcd 651 . . . . 5
4 df-dc 742 . . . . 5 DECID
53, 4sylibr 137 . . . 4 DECID
65a1d 22 . . 3 DECID DECID
7 df-dc 742 . . . . 5 DECID
8 olc 631 . . . . . . . . 9
98adantl 262 . . . . . . . 8
109orcd 651 . . . . . . 7
1110, 4sylibr 137 . . . . . 6 DECID
12 ioran 668 . . . . . . . . 9
1312biimpri 124 . . . . . . . 8
1413olcd 652 . . . . . . 7
1514, 4sylibr 137 . . . . . 6 DECID
1611, 15jaodan 709 . . . . 5 DECID
177, 16sylan2b 271 . . . 4 DECID DECID
1817ex 108 . . 3 DECID DECID
196, 18jaoi 635 . 2 DECID DECID
201, 19sylbi 114 1 DECID DECID DECID
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   wa 97   wo 628  DECID wdc 741
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629
This theorem depends on definitions:  df-bi 110  df-dc 742
This theorem is referenced by:  pm4.55dc  845  pm3.12dc  864  pm3.13dc  865  dn1dc  866  eueq3dc  2709  distrlem4prl  6560  distrlem4pru  6561
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