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Theorem bj-nalset 10015
 Description: nalset 3887 from bounded separation. (Contributed by BJ, 18-Nov-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-nalset
Distinct variable group:   ,

Proof of Theorem bj-nalset
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 alexnim 1539 . 2
2 ax-bdel 9941 . . . . 5 BOUNDED
32ax-bdn 9937 . . . 4 BOUNDED
43bdsep1 10005 . . 3
5 elequ1 1600 . . . . . 6
6 elequ1 1600 . . . . . . 7
7 elequ1 1600 . . . . . . . . 9
8 elequ2 1601 . . . . . . . . 9
97, 8bitrd 177 . . . . . . . 8
109notbid 592 . . . . . . 7
116, 10anbi12d 442 . . . . . 6
125, 11bibi12d 224 . . . . 5
1312spv 1740 . . . 4
14 pclem6 1265 . . . 4
1513, 14syl 14 . . 3
164, 15eximii 1493 . 2
171, 16mpg 1340 1
 Colors of variables: wff set class Syntax hints:   wn 3   wa 97   wb 98  wal 1241  wex 1381 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-in1 544  ax-in2 545  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-4 1400  ax-13 1404  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-bdn 9937  ax-bdel 9941  ax-bdsep 10004 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249  df-nf 1350 This theorem is referenced by:  bj-vprc  10016
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