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Theorem difsnpss 3933
 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 283 . 2
2 difss 3466 . . . 4
32biantrur 493 . . 3
4 difsnb 3932 . . . 4
54necon3bbii 2629 . . 3
6 df-pss 3328 . . 3
73, 5, 63bitr4i 269 . 2
81, 7bitri 241 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 177   wa 359   wcel 1725   wne 2598   cdif 3309   wss 3312   wpss 3313  csn 3806 This theorem is referenced by:  marypha1lem  7430  infpss  8089  ominf4  8184  mrieqv2d  13856 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 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 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-v 2950  df-dif 3315  df-in 3319  df-ss 3326  df-pss 3328  df-sn 3812
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