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Theorem nfraldya 2469
 Description: Not-free for restricted universal quantification where and are distinct. See nfraldxy 2467 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
nfraldya
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)   ()

Proof of Theorem nfraldya
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-ral 2421 . 2
2 sbim 1926 . . . . . 6
3 clelsb3 2244 . . . . . . 7
43imbi1i 237 . . . . . 6
52, 4bitri 183 . . . . 5
65albii 1446 . . . 4
7 nfv 1508 . . . . 5
87sb8 1828 . . . 4
9 df-ral 2421 . . . 4
106, 8, 93bitr4i 211 . . 3
11 nfv 1508 . . . 4
12 nfraldya.3 . . . 4
13 nfraldya.2 . . . . 5
14 nfraldya.4 . . . . 5
1513, 14nfsbd 1950 . . . 4
1611, 12, 15nfraldxy 2467 . . 3
1710, 16nfxfrd 1451 . 2
181, 17nfxfrd 1451 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1329  wnf 1436   wcel 1480  wsb 1735  wnfc 2268  wral 2416 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421 This theorem is referenced by:  nfralya  2473
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