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Theorem nfnel 2747
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  |-  F/_ x A
nfnel.2  |-  F/_ x B
Assertion
Ref Expression
nfnel  |-  F/ x  A  e/  B

Proof of Theorem nfnel
StepHypRef Expression
1 df-nel 2601 . 2  |-  ( A  e/  B  <->  -.  A  e.  B )
2 nfnel.1 . . . 4  |-  F/_ x A
3 nfnel.2 . . . 4  |-  F/_ x B
42, 3nfel 2577 . . 3  |-  F/ x  A  e.  B
54nfn 1929 . 2  |-  F/ x  -.  A  e.  B
61, 5nfxfr 1666 1  |-  F/ x  A  e/  B
Colors of variables: wff setvar class
Syntax hints:   -. wn 3   F/wnf 1637    e. wcel 1842   F/_wnfc 2550    e/ wnel 2599
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-ext 2380
This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-cleq 2394  df-clel 2397  df-nfc 2552  df-nel 2601
This theorem is referenced by: (None)
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