Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  nfrexxy Unicode version

Theorem nfrexxy 2361
 Description: Not-free for restricted existential quantification where and are distinct. See nfrexya 2363 for a version with and distinct instead. (Contributed by Jim Kingdon, 30-May-2018.)
Hypotheses
Ref Expression
nfralxy.1
nfralxy.2
Assertion
Ref Expression
nfrexxy
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem nfrexxy
StepHypRef Expression
1 nftru 1355 . . 3
2 nfralxy.1 . . . 4
32a1i 9 . . 3
4 nfralxy.2 . . . 4
54a1i 9 . . 3
61, 3, 5nfrexdxy 2357 . 2
76trud 1252 1
 Colors of variables: wff set class Syntax hints:   wtru 1244  wnf 1349  wnfc 2165  wrex 2307 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-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312 This theorem is referenced by:  r19.12  2422  sbcrext  2835  nfuni  3586  nfiunxy  3683  rexxpf  4483  abrexex2g  5747  abrexex2  5751  nfrecs  5922  bj-findis  10104  strcollnfALT  10111
 Copyright terms: Public domain W3C validator