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Theorem nfralya 2340
Description: Not-free for restricted universal quantification where and are distinct. See nfralxy 2338 for a version with and distinct instead. (Contributed by Jim Kingdon, 3-Jun-2018.)
Hypotheses
Ref Expression
nfralya.1  F/_
nfralya.2  F/
Assertion
Ref Expression
nfralya  F/
Distinct variable group:   ,
Allowed substitution hints:   (,)   ()

Proof of Theorem nfralya
StepHypRef Expression
1 nftru 1335 . . 3  F/
2 nfralya.1 . . . 4  F/_
32a1i 9 . . 3  F/_
4 nfralya.2 . . . 4  F/
54a1i 9 . . 3  F/
61, 3, 5nfraldya 2336 . 2  F/
76trud 1237 1  F/
Colors of variables: wff set class
Syntax hints:   wtru 1229   F/wnf 1329   F/_wnfc 2147  wral 2284
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 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-cleq 2015  df-clel 2018  df-nfc 2149  df-ral 2289
This theorem is referenced by:  nfiinya  3660
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