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Theorem nfrexdya 2353
Description: Not-free for restricted existential quantification where and are distinct. See nfrexdxy 2351 for a version with and distinct instead. (Contributed by Jim Kingdon, 30-May-2018.)
Hypotheses
Ref Expression
nfraldya.2  F/
nfraldya.3  F/_
nfraldya.4  F/
Assertion
Ref Expression
nfrexdya  F/
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)   ()

Proof of Theorem nfrexdya
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-rex 2306 . 2
2 sban 1826 . . . . . 6
3 clelsb3 2139 . . . . . . 7
43anbi1i 431 . . . . . 6
52, 4bitri 173 . . . . 5
65exbii 1493 . . . 4
7 nfv 1418 . . . . 5  F/
87sb8e 1734 . . . 4
9 df-rex 2306 . . . 4
106, 8, 93bitr4i 201 . . 3
11 nfv 1418 . . . 4  F/
12 nfraldya.3 . . . 4  F/_
13 nfraldya.2 . . . . 5  F/
14 nfraldya.4 . . . . 5  F/
1513, 14nfsbd 1848 . . . 4  F/
1611, 12, 15nfrexdxy 2351 . . 3  F/
1710, 16nfxfrd 1361 . 2  F/
181, 17nfxfrd 1361 1  F/
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   F/wnf 1346  wex 1378   wcel 1390  wsb 1642   F/_wnfc 2162  wrex 2301
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306
This theorem is referenced by:  nfrexya  2357
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