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Theorem nalset 3915
 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 1555 . 2
2 ax-sep 3903 . . 3
3 elequ1 1616 . . . . . 6
4 elequ1 1616 . . . . . . 7
5 elequ1 1616 . . . . . . . . 9
6 elequ2 1617 . . . . . . . . 9
75, 6bitrd 181 . . . . . . . 8
87notbid 602 . . . . . . 7
94, 8anbi12d 450 . . . . . 6
103, 9bibi12d 228 . . . . 5
1110spv 1756 . . . 4
12 pclem6 1281 . . . 4
1311, 12syl 14 . . 3
142, 13eximii 1509 . 2
151, 14mpg 1356 1
 Colors of variables: wff set class Syntax hints:   wn 3   wa 101   wb 102  wal 1257  wex 1397 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-4 1416  ax-13 1420  ax-14 1421  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-sep 3903 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-fal 1265  df-nf 1366 This theorem is referenced by:  vprc  3916
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