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Theorem nalset 4151
 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 alexn 1566 . 2
2 ax-sep 4141 . . 3
3 elequ1 1687 . . . . . . 7
4 elequ1 1687 . . . . . . . 8
5 elequ1 1687 . . . . . . . . . 10
6 elequ2 1689 . . . . . . . . . 10
75, 6bitrd 244 . . . . . . . . 9
87notbid 285 . . . . . . . 8
94, 8anbi12d 691 . . . . . . 7
103, 9bibi12d 312 . . . . . 6
1110spv 1938 . . . . 5
12 pclem6 896 . . . . 5
1311, 12syl 15 . . . 4
1413eximi 1563 . . 3
152, 14ax-mp 8 . 2
161, 15mpgbi 1536 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 176   wa 358  wal 1527  wex 1528   wceq 1623   wcel 1684 This theorem is referenced by:  vprc  4152  kmlem2  7777 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-13 1686  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-sep 4141 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532
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