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Theorem nfrexxy 2470
 Description: Not-free for restricted existential quantification where and are distinct. See nfrexya 2472 for a version with and distinct instead. (Contributed by Jim Kingdon, 30-May-2018.)
Hypotheses
Ref Expression
nfralxy.1
nfralxy.2
Assertion
Ref Expression
nfrexxy
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem nfrexxy
StepHypRef Expression
1 nftru 1442 . . 3
2 nfralxy.1 . . . 4
32a1i 9 . . 3
4 nfralxy.2 . . . 4
54a1i 9 . . 3
61, 3, 5nfrexdxy 2466 . 2
76mptru 1340 1
 Colors of variables: wff set class Syntax hints:   wtru 1332  wnf 1436  wnfc 2266  wrex 2415 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-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-cleq 2130  df-clel 2133  df-nfc 2268  df-rex 2420 This theorem is referenced by:  r19.12  2536  sbcrext  2981  nfuni  3737  nfiunxy  3834  rexxpf  4681  abrexex2g  6011  abrexex2  6015  nfrecs  6197  fimaxre2  10991  nfsum  11119  nfcprod1  11316  nfcprod  11317  bezoutlemmain  11675  ctiunctlemfo  11941  bj-findis  13166  strcollnfALT  13173
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