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Theorem nelrdva 3281
 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 2423 . 2
2 eleq1 2495 . . . . . . 7
32anbi2d 708 . . . . . 6
4 neeq1 2701 . . . . . 6
53, 4imbi12d 321 . . . . 5
6 nelrdva.1 . . . . 5
75, 6vtoclg 3139 . . . 4
87anabsi7 826 . . 3
98neneqd 2621 . 2
101, 9pm2.65da 578 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 370   wceq 1437   wcel 1872   wne 2614 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-12 1909  ax-ext 2401 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-ne 2616  df-v 3082 This theorem is referenced by:  ustfilxp  21226  metustfbas  21571  fourierdlem72  37983
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