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Theorem nss 3489
 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 1720 . . 3
2 dfss2 3420 . . 3
31, 2xchbinxr 313 . 2
43bicomi 206 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 188   wa 371  wal 1441  wex 1662   wcel 1886   wss 3403 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-10 1914  ax-11 1919  ax-12 1932  ax-13 2090  ax-ext 2430 This theorem depends on definitions:  df-bi 189  df-an 373  df-tru 1446  df-ex 1663  df-nf 1667  df-sb 1797  df-clab 2437  df-cleq 2443  df-clel 2446  df-in 3410  df-ss 3417 This theorem is referenced by:  grur1  9242  psslinpr  9453  reclem2pr  9470  mreexexlem2d  15544  prmcyg  17521  filcon  20891  alexsubALTlem4  21058  wilthlem2  23987  shne0i  27094  erdszelem10  29916  fundmpss  30400  relintabex  36181
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