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Theorem nfnel 2890
 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 𝑥𝐴
nfnel.2 𝑥𝐵
Assertion
Ref Expression
nfnel 𝑥 𝐴𝐵

Proof of Theorem nfnel
StepHypRef Expression
1 df-nel 2783 . 2 (𝐴𝐵 ↔ ¬ 𝐴𝐵)
2 nfnel.1 . . . 4 𝑥𝐴
3 nfnel.2 . . . 4 𝑥𝐵
42, 3nfel 2763 . . 3 𝑥 𝐴𝐵
54nfn 1768 . 2 𝑥 ¬ 𝐴𝐵
61, 5nfxfr 1771 1 𝑥 𝐴𝐵
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3  Ⅎwnf 1699   ∈ wcel 1977  Ⅎwnfc 2738   ∉ wnel 2781 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-cleq 2603  df-clel 2606  df-nfc 2740  df-nel 2783 This theorem is referenced by: (None)
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