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Theorem ismkv 7075
 Description: The predicate of being Markov. (Contributed by Jim Kingdon, 18-Mar-2023.)
Assertion
Ref Expression
ismkv Markov
Distinct variable group:   ,,
Allowed substitution hints:   (,)

Proof of Theorem ismkv
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 feq2 5296 . . . 4
2 raleq 2649 . . . . . 6
32notbid 657 . . . . 5
4 rexeq 2650 . . . . 5
53, 4imbi12d 233 . . . 4
61, 5imbi12d 233 . . 3
76albidv 1801 . 2
8 df-markov 7074 . 2 Markov
97, 8elab2g 2855 1 Markov
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 104  wal 1330   wceq 1332   wcel 2125  wral 2432  wrex 2433  c0 3390  wf 5159  cfv 5163  c1o 6346  c2o 6347  Markovcmarkov 7073 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  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-ral 2437  df-rex 2438  df-v 2711  df-fn 5166  df-f 5167  df-markov 7074 This theorem is referenced by:  ismkvmap  7076  omnimkv  7078  mkvprop  7080  omniwomnimkv  7089
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