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Theorem nelrdva 2807
 Description: Deduce negative membership from an implication. (Contributed by Thierry Arnoux, 27-Nov-2017.)
Hypothesis
Ref Expression
nelrdva.1
Assertion
Ref Expression
nelrdva
Distinct variable groups:   ,   ,   ,

Proof of Theorem nelrdva
StepHypRef Expression
1 eqidd 2084 . 2
2 eleq1 2145 . . . . . . 7
32anbi2d 452 . . . . . 6
4 neeq1 2262 . . . . . 6
53, 4imbi12d 232 . . . . 5
6 nelrdva.1 . . . . 5
75, 6vtoclg 2667 . . . 4
87anabsi7 546 . . 3
98neneqd 2270 . 2
101, 9pm2.65da 620 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 102   wceq 1285   wcel 1434   wne 2249 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 2065 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ne 2250  df-v 2612 This theorem is referenced by: (None)
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