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Theorem nfnel 2800
 Description: Bound-variable hypothesis builder for negated membership. (Contributed by David Abernethy, 26-Jun-2011.) (Revised by Mario Carneiro, 7-Oct-2016.)
Hypotheses
Ref Expression
nfnel.1
nfnel.2
Assertion
Ref Expression
nfnel

Proof of Theorem nfnel
StepHypRef Expression
1 df-nel 2655 . 2
2 nfnel.1 . . . 4
3 nfnel.2 . . . 4
42, 3nfel 2632 . . 3
54nfn 1901 . 2
61, 5nfxfr 1645 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  F/wnf 1616  e.wcel 1818  F/_wnfc 2605  e/wnel 2653 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-cleq 2449  df-clel 2452  df-nfc 2607  df-nel 2655
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