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Theorem nfrexya 2449
 Description: Not-free for restricted existential quantification where and are distinct. See nfrexxy 2447 for a version with and distinct instead. (Contributed by Jim Kingdon, 3-Jun-2018.)
Hypotheses
Ref Expression
nfralya.1
nfralya.2
Assertion
Ref Expression
nfrexya
Distinct variable group:   ,
Allowed substitution hints:   (,)   ()

Proof of Theorem nfrexya
StepHypRef Expression
1 nftru 1425 . . 3
2 nfralya.1 . . . 4
32a1i 9 . . 3
4 nfralya.2 . . . 4
54a1i 9 . . 3
61, 3, 5nfrexdya 2445 . 2
76mptru 1323 1
 Colors of variables: wff set class Syntax hints:   wtru 1315  wnf 1419  wnfc 2243  wrex 2392 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-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-cleq 2108  df-clel 2111  df-nfc 2245  df-rex 2397 This theorem is referenced by:  nfiunya  3809  nffrec  6259  nfsup  6845  caucvgsrlemgt1  7567  nfsum1  11076  zsupcllemstep  11545  bezout  11606
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