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

Proof of Theorem nfrexdxy
StepHypRef Expression
1 df-rex 2329 . 2
2 nfraldxy.2 . . 3
3 nfcv 2194 . . . . . 6
43a1i 9 . . . . 5
5 nfraldxy.3 . . . . 5
64, 5nfeld 2209 . . . 4
7 nfraldxy.4 . . . 4
86, 7nfand 1476 . . 3
92, 8nfexd 1660 . 2
101, 9nfxfrd 1380 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101  wnf 1365  wex 1397   wcel 1409  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-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-17 1435  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-nf 1366  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rex 2329 This theorem is referenced by:  nfrexdya  2376  nfrexxy  2378  nfunid  3614  strcollnft  10475
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