Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  nss Unicode version

Theorem nss 3157
 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 1583 . . 3
2 dfss2 3092 . . 3
31, 2xchbinxr 304 . 2
43bicomi 195 1
 Colors of variables: wff set class Syntax hints:   wn 5   wi 6   wb 178   wa 360  wal 1532  wex 1537   wcel 1621   wss 3078 This theorem is referenced by:  grur1  8322  psslinpr  8535  reclem2pr  8552  prmcyg  15015  filcon  17410  alexsubALTlem4  17576  wilthlem2  20139  shne0i  21857  erdszelem10  22902  fundmpss  23290  vxveqv  24219 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-in 3085  df-ss 3089
 Copyright terms: Public domain W3C validator