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Theorem nalset 4341
 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 1590 . 2
2 ax-sep 4331 . . 3
3 elequ1 1729 . . . . . 6
4 elequ1 1729 . . . . . . 7
5 elequ1 1729 . . . . . . . . 9
6 elequ2 1731 . . . . . . . . 9
75, 6bitrd 246 . . . . . . . 8
87notbid 287 . . . . . . 7
94, 8anbi12d 693 . . . . . 6
103, 9bibi12d 314 . . . . 5
1110spv 1966 . . . 4
12 pclem6 898 . . . 4
1311, 12syl 16 . . 3
142, 13eximii 1588 . 2
151, 14mpgbi 1559 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 178   wa 360  wal 1550  wex 1551 This theorem is referenced by:  vprc  4342  kmlem2  8032 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-11 1762  ax-12 1951  ax-sep 4331 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555
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