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Theorem abeq0 3282
 Description: Condition for a class abstraction to be empty. (Contributed by Jim Kingdon, 12-Aug-2018.)
Assertion
Ref Expression
abeq0

Proof of Theorem abeq0
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sbn 1868 . . 3
21albii 1400 . 2
3 nfv 1462 . . 3
43sb8 1778 . 2
5 eq0 3273 . . 3
6 df-clab 2069 . . . . 5
76notbii 627 . . . 4
87albii 1400 . . 3
95, 8bitri 182 . 2
102, 4, 93bitr4ri 211 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 103  wal 1283   wceq 1285   wcel 1434  wsb 1686  cab 2068  c0 3258 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  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-fal 1291  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-dif 2976  df-nul 3259 This theorem is referenced by:  opprc  3599
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