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Theorem nfnel 2704
 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 2604 . 2
2 nfnel.1 . . . 4
3 nfnel.2 . . . 4
42, 3nfel 2582 . . 3
54nfn 1812 . 2
61, 5nfxfr 1580 1
 Colors of variables: wff set class Syntax hints:   wn 3  wnf 1554   wcel 1726  wnfc 2561   wnel 2602 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-cleq 2431  df-clel 2434  df-nfc 2563  df-nel 2604
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