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Theorem nssss 4419
 Description: Negation of subclass relationship. Compare nss 3406. (Contributed by NM, 30-Jun-2004.) (Proof shortened by Andrew Salmon, 25-Jul-2011.)
Assertion
Ref Expression
nssss
Distinct variable groups:   ,   ,

Proof of Theorem nssss
StepHypRef Expression
1 exanali 1595 . . 3
2 ssextss 4417 . . 3
31, 2xchbinxr 303 . 2
43bicomi 194 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wa 359  wal 1549  wex 1550   wss 3320 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-pw 3801  df-sn 3820  df-pr 3821
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