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Theorem nfdisjv 3785
 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 3775 . 2 Disj
2 nfcv 2194 . . . . . 6
3 nfdisjv.1 . . . . . 6
42, 3nfel 2202 . . . . 5
5 nfdisjv.2 . . . . . 6
65nfcri 2188 . . . . 5
74, 6nfan 1473 . . . 4
87nfmo 1936 . . 3
98nfal 1484 . 2
101, 9nfxfr 1379 1 Disj
 Colors of variables: wff set class Syntax hints:   wa 101  wal 1257  wnf 1365   wcel 1409  wmo 1917  wnfc 2181  Disj wdisj 3773 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-eu 1919  df-mo 1920  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rmo 2331  df-disj 3774 This theorem is referenced by: (None)
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