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Theorem nssinpss 3163
Description: Negation of subclass expressed in terms of intersection and proper subclass. (Contributed by NM, 30-Jun-2004.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
nssinpss  C_  i^i  C.

Proof of Theorem nssinpss
StepHypRef Expression
1 inss1 3151 . . 3  i^i  C_
21biantrur 287 . 2  i^i  =/=  i^i 
C_  i^i  =/=
3 df-ss 2925 . . 3 
C_  i^i
43necon3bbii 2236 . 2  C_  i^i  =/=
5 df-pss 2927 . 2  i^i  C.  i^i  C_  i^i  =/=
62, 4, 53bitr4i 201 1  C_  i^i  C.
Colors of variables: wff set class
Syntax hints:   wn 3   wa 97   wb 98    =/= wne 2201    i^i cin 2910    C_ wss 2911    C. wpss 2912
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ne 2203  df-v 2553  df-in 2918  df-ss 2925  df-pss 2927
This theorem is referenced by: (None)
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