Mathbox for BJ < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  bj-nalset Structured version   Unicode version

Theorem bj-nalset 9326
 Description: nalset 3878 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 1536 . 2
2 ax-bdel 9256 . . . . 5 BOUNDED
32ax-bdn 9252 . . . 4 BOUNDED
43bdsep2 9320 . . 3
5 elequ1 1597 . . . . . 6
6 elequ1 1597 . . . . . . 7
7 elequ1 1597 . . . . . . . . 9
8 elequ2 1598 . . . . . . . . 9
97, 8bitrd 177 . . . . . . . 8
109notbid 591 . . . . . . 7
116, 10anbi12d 442 . . . . . 6
125, 11bibi12d 224 . . . . 5
1312spv 1737 . . . 4
14 pclem6 1264 . . . 4
1513, 14syl 14 . . 3
164, 15eximii 1490 . 2
171, 16mpg 1337 1
 Colors of variables: wff set class Syntax hints:   wn 3   wa 97   wb 98  wal 1240  wex 1378 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 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-13 1401  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-ext 2019  ax-bdn 9252  ax-bdel 9256  ax-bdsep 9319 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248  df-nf 1347  df-cleq 2030  df-clel 2033 This theorem is referenced by:  bj-vprc  9327
 Copyright terms: Public domain W3C validator