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Theorem dcan 841
Description: A conjunction of two decidable propositions is decidable. (Contributed by Jim Kingdon, 12-Apr-2018.)
Assertion
Ref Expression
dcan DECID DECID DECID

Proof of Theorem dcan
StepHypRef Expression
1 simpl 102 . . . . . 6
21intnanrd 840 . . . . 5
32orim2i 677 . . . 4
4 simpr 103 . . . . . 6
54intnand 839 . . . . 5
65olcd 652 . . . 4
73, 6jaoi 635 . . 3
8 df-dc 742 . . . . 5 DECID
9 df-dc 742 . . . . 5 DECID
108, 9anbi12i 433 . . . 4 DECID DECID
11 andi 730 . . . 4
12 andir 731 . . . . 5
1312orbi1i 679 . . . 4
1410, 11, 133bitri 195 . . 3 DECID DECID
15 df-dc 742 . . 3 DECID
167, 14, 153imtr4i 190 . 2 DECID DECID DECID
1716ex 108 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:  dcbi  843  annimdc  844  pm4.55dc  845  anordc  862  xordidc  1287  nn0n0n1ge2b  8096
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