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Theorem nfrexdya 2376
 Description: Not-free for restricted existential quantification where and are distinct. See nfrexdxy 2374 for a version with and distinct instead. (Contributed by Jim Kingdon, 30-May-2018.)
Hypotheses
Ref Expression
nfraldya.2
nfraldya.3
nfraldya.4
Assertion
Ref Expression
nfrexdya
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)   ()

Proof of Theorem nfrexdya
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-rex 2329 . 2
2 sban 1845 . . . . . 6
3 clelsb3 2158 . . . . . . 7
43anbi1i 439 . . . . . 6
52, 4bitri 177 . . . . 5
65exbii 1512 . . . 4
7 nfv 1437 . . . . 5
87sb8e 1753 . . . 4
9 df-rex 2329 . . . 4
106, 8, 93bitr4i 205 . . 3
11 nfv 1437 . . . 4
12 nfraldya.3 . . . 4
13 nfraldya.2 . . . . 5
14 nfraldya.4 . . . . 5
1513, 14nfsbd 1867 . . . 4
1611, 12, 15nfrexdxy 2374 . . 3
1710, 16nfxfrd 1380 . 2
181, 17nfxfrd 1380 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101  wnf 1365  wex 1397   wcel 1409  wsb 1661  wnfc 2181  wrex 2324 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-nf 1366  df-sb 1662  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rex 2329 This theorem is referenced by:  nfrexya  2380
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