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Theorem nss 3561
Description: Negation of subclass relationship. Exercise 13 of [TakeutiZaring] p. 18. (Contributed by NM, 25-Feb-1996.) (Proof shortened by Andrew Salmon, 21-Jun-2011.)
Assertion
Ref Expression
nss
Distinct variable groups:   ,   ,

Proof of Theorem nss
StepHypRef Expression
1 exanali 1670 . . 3
2 dfss2 3492 . . 3
31, 2xchbinxr 311 . 2
43bicomi 202 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  E.wex 1612  e.wcel 1818  C_wss 3475
This theorem is referenced by:  grur1  9219  psslinpr  9430  reclem2pr  9447  mreexexlem2d  15042  prmcyg  16896  filcon  20384  alexsubALTlem4  20550  wilthlem2  23343  shne0i  26366  erdszelem10  28644  fundmpss  29196
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-in 3482  df-ss 3489
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