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Theorem stabtestimpdc 824
 Description: "Stable and testable" is equivalent to decidable. (Contributed by David A. Wheeler, 13-Aug-2018.)
Assertion
Ref Expression
stabtestimpdc STAB DECID DECID

Proof of Theorem stabtestimpdc
StepHypRef Expression
1 exmiddc 744 . . . . . 6 DECID
21adantl 262 . . . . 5 STAB DECID
3 df-stab 740 . . . . . . . 8 STAB
43biimpi 113 . . . . . . 7 STAB
54orim2d 702 . . . . . 6 STAB
65adantr 261 . . . . 5 STAB DECID
72, 6mpd 13 . . . 4 STAB DECID
87orcomd 648 . . 3 STAB DECID
9 df-dc 743 . . 3 DECID
108, 9sylibr 137 . 2 STAB DECID DECID
11 dcimpstab 752 . . 3 DECID STAB
12 dcn 746 . . 3 DECID DECID
1311, 12jca 290 . 2 DECID STAB DECID
1410, 13impbii 117 1 STAB DECID DECID
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 97   wb 98   wo 629  STAB wstab 739  DECID wdc 742 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 630 This theorem depends on definitions:  df-bi 110  df-stab 740  df-dc 743 This theorem is referenced by: (None)
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