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Theorem difsnpss 4173
Description: is a proper subclass of if and only if is a member of . (Contributed by David Moews, 1-May-2017.)
Assertion
Ref Expression
difsnpss

Proof of Theorem difsnpss
StepHypRef Expression
1 notnot 291 . 2
2 difss 3630 . . . 4
32biantrur 506 . . 3
4 difsnb 4172 . . . 4
54necon3bbii 2718 . . 3
6 df-pss 3491 . . 3
73, 5, 63bitr4i 277 . 2
81, 7bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  <->wb 184  /\wa 369  e.wcel 1818  =/=wne 2652  \cdif 3472  C_wss 3475  C.wpss 3476  {csn 4029
This theorem is referenced by:  marypha1lem  7913  infpss  8618  ominf4  8713  mrieqv2d  15036
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-nfc 2607  df-ne 2654  df-v 3111  df-dif 3478  df-in 3482  df-ss 3489  df-pss 3491  df-sn 4030
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