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Theorem difsnpss 4111
 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 3578 . . . 4
32biantrur 506 . . 3
4 difsnb 4110 . . . 4
54necon3bbii 2707 . . 3
6 df-pss 3439 . . 3
73, 5, 63bitr4i 277 . 2
81, 7bitri 249 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wb 184   wa 369   wcel 1758   wne 2642   cdif 3420   wss 3423   wpss 3424  csn 3972 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-ext 2430 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2599  df-ne 2644  df-v 3067  df-dif 3426  df-in 3430  df-ss 3437  df-pss 3439  df-sn 3973 This theorem is referenced by:  marypha1lem  7781  infpss  8484  ominf4  8579  mrieqv2d  14676
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