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Theorem nalset 3878
Description: No set contains all sets. Theorem 41 of [Suppes] p. 30. (Contributed by NM, 23-Aug-1993.)
Assertion
Ref Expression
nalset
Distinct variable group:   ,

Proof of Theorem nalset
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 alexnim 1536 . 2
2 ax-sep 3866 . . 3
3 elequ1 1597 . . . . . 6
4 elequ1 1597 . . . . . . 7
5 elequ1 1597 . . . . . . . . 9
6 elequ2 1598 . . . . . . . . 9
75, 6bitrd 177 . . . . . . . 8
87notbid 591 . . . . . . 7
94, 8anbi12d 442 . . . . . 6
103, 9bibi12d 224 . . . . 5
1110spv 1737 . . . 4
12 pclem6 1264 . . . 4
1311, 12syl 14 . . 3
142, 13eximii 1490 . 2
151, 14mpg 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-sep 3866
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248  df-nf 1347
This theorem is referenced by:  vprc  3879
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