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Theorem nfeudv 1912
Description: Deduction version of nfeu 1916. Similar to nfeud 1913 but has the additional constraint that and must be distinct. (Contributed by Jim Kingdon, 25-May-2018.)
Hypotheses
Ref Expression
nfeudv.1  F/
nfeudv.2  F/
Assertion
Ref Expression
nfeudv  F/
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem nfeudv
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1418 . . 3  F/
2 nfeudv.1 . . . 4  F/
3 nfeudv.2 . . . . 5  F/
4 nfv 1418 . . . . . 6  F/
54a1i 9 . . . . 5  F/
63, 5nfbid 1477 . . . 4  F/
72, 6nfald 1640 . . 3  F/
81, 7nfexd 1641 . 2  F/
9 df-eu 1900 . . 3
109nfbii 1359 . 2  F/  F/
118, 10sylibr 137 1  F/
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98  wal 1240   wceq 1242   F/wnf 1346  wex 1378  weu 1897
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-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-eu 1900
This theorem is referenced by:  nfeud  1913
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