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Theorem nfralya 2445
 Description: Not-free for restricted universal quantification where and are distinct. See nfralxy 2443 for a version with and distinct instead. (Contributed by Jim Kingdon, 3-Jun-2018.)
Hypotheses
Ref Expression
nfralya.1
nfralya.2
Assertion
Ref Expression
nfralya
Distinct variable group:   ,
Allowed substitution hints:   (,)   ()

Proof of Theorem nfralya
StepHypRef Expression
1 nftru 1423 . . 3
2 nfralya.1 . . . 4
32a1i 9 . . 3
4 nfralya.2 . . . 4
54a1i 9 . . 3
61, 3, 5nfraldya 2441 . 2
76mptru 1321 1
 Colors of variables: wff set class Syntax hints:   wtru 1313  wnf 1417  wnfc 2240  wral 2388 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1404  ax-7 1405  ax-gen 1406  ax-ie1 1450  ax-ie2 1451  ax-8 1463  ax-10 1464  ax-11 1465  ax-i12 1466  ax-bndl 1467  ax-4 1468  ax-17 1487  ax-i9 1491  ax-ial 1495  ax-i5r 1496  ax-ext 2095 This theorem depends on definitions:  df-bi 116  df-tru 1315  df-nf 1418  df-sb 1717  df-cleq 2106  df-clel 2109  df-nfc 2242  df-ral 2393 This theorem is referenced by:  nfiinya  3806  nfsup  6828  caucvgsrlemgt1  7530  supinfneg  9285  infsupneg  9286  ctiunctlemudc  11786
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