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Theorem nfdisjv 3748
 Description: Bound-variable hypothesis builder for disjoint collection. (Contributed by Jim Kingdon, 19-Aug-2018.)
Hypotheses
Ref Expression
nfdisjv.1
nfdisjv.2
Assertion
Ref Expression
nfdisjv Disj
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem nfdisjv
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfdisj2 3738 . 2 Disj
2 nfcv 2175 . . . . . 6
3 nfdisjv.1 . . . . . 6
42, 3nfel 2183 . . . . 5
5 nfdisjv.2 . . . . . 6
65nfcri 2169 . . . . 5
74, 6nfan 1454 . . . 4
87nfmo 1917 . . 3
98nfal 1465 . 2
101, 9nfxfr 1360 1 Disj
 Colors of variables: wff set class Syntax hints:   wa 97  wal 1240  wnf 1346   wcel 1390  wmo 1898  wnfc 2162  Disj wdisj 3736 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-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rmo 2308  df-disj 3737 This theorem is referenced by: (None)
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