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Theorem nfned 2292
Description: Bound-variable hypothesis builder for inequality. (Contributed by NM, 10-Nov-2007.) (Revised by Mario Carneiro, 7-Oct-2016.)
Hypotheses
Ref Expression
nfned.1  F/_
nfned.2  F/_
Assertion
Ref Expression
nfned  F/  =/=

Proof of Theorem nfned
StepHypRef Expression
1 df-ne 2203 . 2  =/=
2 nfned.1 . . . 4  F/_
3 nfned.2 . . . 4  F/_
42, 3nfeqd 2189 . . 3  F/
54nfnd 1544 . 2  F/
61, 5nfxfrd 1361 1  F/  =/=
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   wceq 1242   F/wnf 1346   F/_wnfc 2162    =/= wne 2201
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248  df-nf 1347  df-cleq 2030  df-nfc 2164  df-ne 2203
This theorem is referenced by: (None)
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