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Theorem nelrdva 2919
 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 2158 . 2
2 eleq1 2220 . . . . . . 7
32anbi2d 460 . . . . . 6
4 neeq1 2340 . . . . . 6
53, 4imbi12d 233 . . . . 5
6 nelrdva.1 . . . . 5
75, 6vtoclg 2772 . . . 4
87anabsi7 571 . . 3
98neneqd 2348 . 2
101, 9pm2.65da 651 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 103   wceq 1335   wcel 2128   wne 2327 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 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-ne 2328  df-v 2714 This theorem is referenced by: (None)
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